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Mathomatic User Guide

1. If you have Invariant Sections Front Cover Texts and Back Cover Texts replace the with Texts line with this with the Invariant Sections being LIST THEIR TITLES with the 10 FUTURE REVISIONS OF THIS LICENSE 59 GNU Free Documentation License 10 23 2012 Front Cover Texts being LIST and with the Back Cover Texts being LIST If you have Invariant Sections without Cover Texts or some other combination of the three merge those two alternatives to suit the situation If your document contains nontrivial examples of program code we recommend releasing these examples in parallel under your choice of free software license such as the GNU General Public License to permit their use in free software ADDENDUM How to use this License for your d uments
2. Repeat command 41 Mathomatic Command Reference 10 23 2012 The polar coordinates before root taking are 8 amplitude and 0 radians 0 degrees The 3 roots of 8 1 3 are 2 Inverse check 8 1 1 73205080757 i Inverse check 8 1 1 73205080757 i Inverse check 8 I gt repeat roots repeatedly prompts for all input performing its function again and again until empty lines are given Save command Syntax save file name This command saves all expressions in all equation spaces into the specified text file If the file exists Mathomatic will ask you if you want to overwrite it The saved expressions and equations can be reloaded restored at a later time by using the read command You can edit the saved expressions with your favorite ASCII text editor Another way to save all equation spaces exactly as they are is to enter list hex all gt filename into the main Mathomatic prompt however this saves all constants in hexadecimal and it always overwrites filename Because internally constants are binary hexadecimal can represent them exactly Reading in the result of this list hex command should result in exactly the same expressions in the same numbered equation spaces The save command does not save the associated equation number it only saves all of your equations and expressions It is much easier to read and edit than list hex If you have done anything you want to keep be sure and s
3. 2 x 2 3x 4 2 gt factor Horner factoring 2 x x x 2 3 4 Factor command 28 Mathomatic Command Reference 10 23 2012 factor power does only power operator collecting that is a n a m b n b m is transformed to a b n m With this option variables cannot be specified To undo any kind of factoring in selected equation spaces use the unfactor command For command Syntax for variable start end step size Alternate syntax for variable start to end step step size This command is good for testing an expression with many sequential input values It quickly evaluates approximates simplifies and displays the current expression for each value of the index variable as the index variable goes from start to end in steps of step size default 1 Nothing is modified The syntax of this command is the same as the sum and product commands This command is not a programming construct and only allows automatically plugging in sequential values of a variable into the current expression approximating and simplifying then displaying the results in single line format Fraction command Syntax fraction numerator denominator equation number range This command reduces and converts expressions with any algebraic fractions in them into a single simple algebraic fraction usually the ratio of two polynomials similar to what Maxima s rat and rat simp functions do It
4. factorial same as gamma x 1 function highest precedence or power exponentiation high precedence multiply divide modulus integral divide add subtract or negate equate denotes equivalence lowest precedence Higher precedence operators are grouped or evaluated first then multiple operators of the same precedence level are grouped left to right This is called the order of operations To group power operators from right to left like most math programs do enter set right_associative_power at the main prompt The default operator is multiply If an expression operand is entered when an operator is expected a multiply operator is automatically inserted For example entering 2x 2 x 2 x and 2 x all result in the Variables 8 Mathomatic User Guide 10 23 2012 expression 2 x The modulus operator a b spoken as a modulo b gives the remainder of the division a b which allows modular arithmetic also known as clock arithmetic because the numbers wrap around after they reach the modulus Mathomatic can simplify calculate and sometimes even solve modular arithmetic Using integer variables allows further modulus simplification when using the simplify command An integer variable is specified by using a variable name that starts with integer like integer1 integer_x etc The resulting sign of any numerical modulus operation depends upon the set modulus_mode option The
5. integrate definite also integrates but prompts you for the lower and upper bounds for definite integration The bounds may also be specified on the end of the command line If g x is the indefinite integral antiderivative of f x the definite integral is g upper_bound g lower_bound Specifying the order allows you to repeatedly integrate The default is to integrate once order 1 This command is only capable of integrating polynomials I KS 2FL le 3 2 2 x 1 1 gt integrate x x 4 2 3 x 2 2 x 4 3 2 2 gt derivative x check the result Differentiating with respect to x and simplifying 3 x 3 x2 x 1 3 gt compare 1 Comparing 1 with 3 Expressions are identical 3 gt Laplace command Syntax laplace inverse variable Integrate command 32 Mathomatic Command Reference 10 23 2012 This command computes the Laplace transform of a polynomial function of the specified variable using the current expression or RHS of the current equation as the function If successful the transformed function is placed in the next available equation space displayed and becomes the current equation This command only works with polynomials A Laplace transform can be undone by applying the inverse Laplace transform That is accomplished by specifying the inverse option to this command gt y 1 1 y 1 1 gt laplace x compute the Laplace t
6. Automatic cubic third degree quintic fifth degree and higher degree polynomial equation solving is not supported Some cubic and quartic polynomial equations can be manually solved with the general equations in files tests cubic in and tests quartic in Quartic fourth degree polynomial equations can be automatically solved if they are biquadratic that is containing only degree four degree two and degree zero terms of the solve variable Biquadratic polynomial equations of any degree can be generally solved by Mathomatic because they can be plugged into the quadratic formula Note that running the simplify command is a good idea after solving The solve routine only unfactors the equation as needed to solve it and the result is not completely simplified To solve for zero type in 0 at the main prompt Zero solving is a special solve that will always be successful and will transform most divide operators into mathematically equivalent multiplications and subtractions so that the result will more likely be a valid polynomial equation 1 gt a b 1 b This is actually a quadratic equation 1 ls a BS 1 gt 0 Solve for the constant zero 1s OS b b ay 41 1 gt unfactor Expand showing this is a quadratic polynomial equation in b 1 0 b 2 b a 1 1 gt b Solve for variable b Equation was quadratic 1 Elas 4 sagnl a 2 1 b 2 1 gt a Solve back for varia
7. Note that the Mathomatic Symbolic Math Library does not support use of the calculate command at this time set no autoselect will turn off selecting of equation spaces by just typing in the equation number Selecting is still possible using the operator Set command 43 Mathomatic Command Reference 10 23 2012 set auto and set no auto turn on and off all three of the above auto options at once If turned off all expressions entered at the main prompt will be entered into equation spaces so they can be operated on by Mathomatic commands set debug followed by an integer sets the debug level number The initial debug level is 0 for no debugging If the level number is 2 set debug 2 Mathomatic will show you how it solves equations Level 4 debugs the simplify command and its polynomial routines Levels 5 and 6 show all intermediate expressions Set the debug level to 1 for suppression of helpful messages or set the debug level to 2 to even suppress warnings set case_sensitive will set alphabetic case sensitive mode while set no case will set case insensitive mode all alphabetic characters will be converted to lower case set case is the default set color enables color mode which is the default When color mode is on ANSI color escape sequences are output to make expressions easier to read Requires a terminal emulator that supports ANSI color escape sequences Enter set save no color to always startup M
8. Solving Equations 17 Mathomatic Command Reference 10 23 2012 Approximate command Syntax approximate equation number ranges This command approximates all real and complex number constants in the current or specified equation spaces It substitutes the special universal constants pi and e with their respective double precision floating point values and approximates all real and imaginary constants roots and surds to be of double precision size This allows them to combine with other double precision floating point constants through standard or complex number arithmetic and may help with simplification and comparisons The result may contain fractions unless set no fractions was entered previously repeat approximate approximates and simplifies even more as much as the calculate command does Calculate command Syntax calculate factor equation number range feedback variable number of iterations This is the formula calculator command that prompts for the value of each normal variable in the RHS of the current or specified equations or in the current or specified expressions temporarily substituting any entered values when not in test or demo mode Test and demo modes allow for no user intervention This calculate command approximates simplifies and substitutes all sign variables with all possible combinations of values 1 and 1 approximating simplifying again and displaying each solution as it does so If all vari
9. x1 x2 2 yl y2 2 1 gt distance 2 L 2 z1 z2 2 Add another leg 2 distance 2 L 2 zl 22 2 2 gt eliminate L Combine the two equations Solving equation 1 for L and substituting into the current equation 2 distance 2 x1 x2 2 yl y2 2 z21 22 2 2 gt distance Solve to get the distance formula for 3D space I 2 distance x1 x2 2 yl y2 2 zl z2 2 sign2 2 Finished reading file pyth3d in 2 gt Eliminate command 26 Mathomatic Command Reference 10 23 2012 Extrema command Syntax extrema variable order This command computes possible extrema the minimums and maximums of the current expression by default or possible inflection points when order is 2 The result is placed in the next available equation space displayed and becomes the current equation The original expression is not modified By default order 1 this command computes stationary points The stationary points of function f x are the values of x when the slope derivative equals zero Stationary points are likely the local minimums and maximums of the function unless the point is determined to be an inflection point For y f x where f x is the RHS and x is the specified variable this command gives the values of x that make the minimums and maximums of y This is computed by taking the derivative of f x setting it equal to zero and then solving for x The
10. Taylor series uses differentiation and is often used to approximate expressions near the specified point The Taylor series of f x at point a is the power series 2 3 f a x a a x a EE Ca 2 a 1 at 3 Sum command 49 Mathomatic Command Reference 10 23 2012 where f x is the first derivative of f x with respect to x f x is the second derivative etc This command prompts you for the point of expansion which is usually a variable or 0 but may be any expression Typically 0 is used to generate Maclaurin polynomials Then it prompts you for the order of the series which is an integer indicating how many derivatives to take in the expansion The default is a large number stopping when the derivative reaches 0 The result is simplified unless the nosimplify option is specified and placed in the next available equation space displayed and becomes the current equation The original expression is not modified 1 gt e x 1 e x 1 gt taylor x Taylor series expansion around x point Enter point 0 Enter order number of derivatives to take 8 Computing the Taylor series and simplifying 8 derivatives applied x 2 x 3 x 4 x 5 x6 KAT x 8 2 1 xt 2 6 24 120 720 5040 40320 Unfactor command Syntax unfactor count fraction quick power equation number range Alternate command name expand This command algebraically expands expressions in
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13. does this by combining all terms added together with like and unlike denominators to a single simple fraction with a like denominator Unlike denominators are combined by converting the terms to what they would be over like common denominators Fractions are reduced by cancelling out the Greatest Common Divisor GCD of the numerator and denominator The result of this command is mathematically equivalent to the original expression unless the numerator or denominator option is specified in which case the result is the numerator or denominator of the original expression If both the numerator and denominator options are specified at once this command will return with failure if the result is not a fraction otherwise the entire fraction is returned Note that algebraic fractions added together with like denominators are automatically combined by almost any Mathomatic command Polynomial factoring is only done by the simplify command and this fraction command to improve simplification Example For command 29 Mathomatic Command Reference 10 23 2012 1 gt 1 x 1 y 1 z 1 1 1 Dig a ep x y Z 1 gt fraction y x z x y xyz 1 gt unfactor y z zz x y x y z 1 gt unfactor fraction 1 1 li Seta x y Zz repeat fraction repeatedly runs the fraction command until the result stabilizes to the smallest size simple algebraic fraction If more simplificatio
14. if available and security is off The matho primes command line is specified instead of equation number ranges list primes all will continually output consecutive primes The matho primes output can be redirected This list command simply outputs expressions and equations as stored internally by Mathomatic translating them to the requested output format There is no simplification and nothing more is done list primes performs a different function and is just short hand for typing matho primes at the shell prompt To pretty print and display equation spaces in better looking multi line fraction format use the display command Nintegrate command Syntax nintegrate trapezoid variable partitions lower and upper bounds This is a numerical integrate command that will work with almost any expression and will not generally compute the exact symbolic integral except for the simplest of expressions This command will prompt you for the lower and upper bounds to perform numerical definite integration on the current expression or the RHS of the current equation with respect to the specified variable These bounds may be any expression not containing infinity and may be entered at the end of the command line following partitions separated by spaces or commas This command uses Simpson s rule to do the approximation Accuracy varies widely depending on the expression integrated the interval between the lower and upper bounds and the
15. integral divide operator a b divides a by b and then truncates by zeroing the fractional part to make the result an integer For example 8 3 results in 2 which is useful when doing integer arithmetic This operator currently implements no rules of algebra and will not evaluate if an operand is a complex number Factorials x use the gamma function gamma x 1 so that the factorial operator works with any real number not just the positive integers The factorial operator currently implements no rules of algebra and will not evaluate for complex numbers or if an overflow happens Absolute value notation is allowed Ixl is always converted to x 2 5 This is not the same as standard absolute value where the real and imaginary parts of complex numbers are separated out and then plugged into the distance formula the Pythagorean theorem returning a real distance value but it works the same when given real number values with no imaginary units The absolute value operation Ixl results in a positive value for any x value that is if 1 is a factor it is removed With Mathomatic if x is imaginary you may get an unwanted imaginary result but it will be positive Order of Operations example The following example shows why operator precedence is important Given the numerical expression 64 2 4 6 3 1 Mathomatic will parenthesize the highest precedence operators first power then times and divide Addition and subtraction are the
16. lowest precedence so no need to parenthesize them The result will be 64 2 4 6 3 1 This is evaluated by combining constants from left to right on the same level of parentheses deepest levels first So the calculations are performed in the following order 64 16 6 4 Combine deepest level parentheses first 4 24 Divided 64 by 16 and multiplied 6 by 4 28 Added 24 to 4 If the calculations were performed in a different order the result would be different Operators 9 Mathomatic User Guide 10 23 2012 Complex Numbers Mathomatic automatically performs complex number addition subtraction multiplication division and exponentiation It can also approximate roots of real and complex numbers giving a single result when multiple results are possible the first real number result is chosen To view all roots of a complex number use the roots command Complex numbers are usually of the form a b i where a is the real part a real number and b is the imaginary part an imaginary number iis the imaginary unit and it represents the square root of 1 1 5 in Mathomatic notation additionally sqrt 1 in m4 Mathomatic notation a t D L is the rectangular coordinate form of a complex number To view the polar coordinate form use the roots command The imaginary unit i may appear anywhere within an expression as many times as you want Mathomatic will handle and simplify it properly As a
17. modified After this command the pushed expressions are accessed by pressing the cursor UP up arrow key If any one of the arguments is not a valid equation number range the text string containing all arguments is pushed into the readline history Plot command 38 Mathomatic Command Reference 10 23 2012 This command only exists if Mathomatic was compiled with readline support Quit command Syntax quit exit value Alternate command name exit Type in this command to exit Mathomatic All expressions in memory are discarded To save all your expressions stored in equation spaces use the save command before quitting The optional decimal exit value argument is the exit status returned to the operating system The default is 0 meaning OK Another way to quickly exit Mathomatic is to enter your operating system s End Of File EOF character at the beginning of an input line The EOF character for Unix like operating systems is Control D Read command Syntax read file name or directory This command reads in a text file as if you typed the text of the file in at the main prompt The text file also known as a script should contain Mathomatic expressions and commands Read commands may be nested that is the file read in may contain further read commands If any command or operation returns with an error all current read operations are aborted this can be prevented by starting the line that returns with error with a co
18. number of derivatives to take before solving can be specified by the order argument default is 1 When order is 2 possible points of inflection are determined A point of inflection is a point on a curve at which the second derivative changes sign from positive to negative or negative to positive 1 gt y x 2 1 y x 2 1 gt extrema x This function is a parabola with the minimum at x 0 Factor command Syntax factor number integers or power equation number range variables Alternate command name collect This command will factorize manually entered integers displaying all prime factors when numbers is specified on the factor command line Otherwise this command will factor variables in expressions in the specified equation spaces and factor out the GCD of rational constant coefficients resulting in smaller integer coefficients This is a very handy command for your algebraic manipulation toolbox This command does not factor polynomials To factor polynomials with repeated or symbolic factors use the simplify or fraction commands To factorize integers in equation spaces and display use the display factor Extrema command 27 Mathomatic Command Reference 10 23 2012 command or set factor_integers command to always do this factor number will prompt for integers to factorize which may be up to 15 decimal digits Preceding this command with repeat or using the plural factor numbers will rep
19. number of partitions The default is to split the interval into 1000 partitions Setting the number of partitions greater than 10000 seldom is helpful because of accumulated floating point round off error If trapezoid is specified on the command line the trapezoid method is used instead which is usually less accurate than Simpson s rule The way the trapezoid method works is the interval from the lower bound to the upper bound is divided into 1000 partitions to produce 1000 trapezoids then the area of each trapezoid is added together to produce the result This means that the accuracy usually decreases as the interval increases Simpson s rule uses the same method with quadratic curves bounding the top of each trapezoid instead of straight lines so that curves are approximated better If the integration fails chances of success are greater if you reduce the number of variables involved in the integration If there are any singularities such as division by zero between the bounds of integration the computed result will be wrong Formatting options 35 Mathomatic Command Reference 10 23 2012 Here is an example of successful numerical integration 1 gt y x 0 5 1 x 3 1 gt nintegrate x Warning Singularity detected result of numerical integration might be wrong Enter lower bound 2 Enter upper bound 4 Approximating the definite integral of the RHS using Simpson s rule 1000 partitions umerical integrati
20. original documents forming one section Entitled History likewise combine any sections Entitled Acknowledgements and any sections Entitled Dedications You must delete all sections Entitled Endorsements 6 COLLECTIONS OF DOCUMENTS You may make a collection consisting of the Document and other documents released under this License and replace the individual copies of this License in the various documents with a single copy that is included in the collection provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects You may extract a single document from such a collection and distribute it individually under this License provided you insert a copy of this License into the extracted document and follow this License in all other respects regarding verbatim copying of that document 7 AGGREGATION WITH INDEPENDENT WORKS A compilation of the Document or its derivatives with other separate and independent documents or works in or on a volume of a storage or distribution medium is called an aggregate if the copyright resulting from the compilation is not used to limit the legal rights of the compilation s users beyond what the individual works permit When the Document is included in an aggregate this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document 5 COMBINING DOCUMENTS 57 GNU Free Documentation Li
21. screen size and always displays in fraction format which is useful for a terminal that doesn t wrap lines In most cases this value is set automatically to be the correct width on startup or by typing set columns This value only affects 2D expression output set wide sets the number of screen columns like set columns 0 above does and screen rows to 0 so that no checking for screen size is done forcing 2D display of expressions that Options 44 Mathomatic Command Reference 10 23 2012 are too wide to display properly on a terminal with line wrap Setting this option is useful if output is going to a file set no display2d will set the expression display mode to single line format one dimensional using the list command instead of the default fraction format two dimensional using the display command Single line format is useful when feeding Mathomatic output into another program fractions_display_mode is a new set option that allows controlling whether or not to display numerical fractions It also can set the preference of simple or mixed fractions The Mathomatic default is to display simple fractions set no fractions_display sets the mode to 0 disabling the automatic conversion of non integer constants like 5 to 1 2 for display set fractions simple means display some constants like 5 and 2 25 as their simple fraction equivalents 1 2 and 9 4 set fractions mixed means display some constants as mixed or si
22. the real number part see the real command The separation variable may be specified on the command line the default is the imaginary unit i i is really a mathematical constant equal to the square root of 1 but it can often be specified where variables are required in Mathomatic If successful the result may contain the imaginary unit i or the specified separation variable 1 gt atb i ctd i 1 gt imaginary i b c a d 2 GP eo 2422 2 gt To remove i from the result type replace i with 1 Integrate command Syntax integrate constant or definite variable order lower and upper bounds Alternate command name integral Help command 31 Mathomatic Command Reference 10 23 2012 This command computes the exact symbolic integral of a polynomial function with respect to the specified variable using the current expression or RHS of the current equation as the function If successful the simplified integral is placed in the next available equation space displayed and becomes the current equation The default is to compute and display the indefinite integral also known as the antiderivative or primitive The antiderivative is the inverse transformation of the derivative integrate constant simply adds a sequentially named constant of integration C_1 C_2 etc to each integration result The constants of integration here are actually variables that may be set to any constant
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24. Mathomatic User Guide George Gesslein II 1987 2012 George Gesslein II Mathomatic User Guide 10 23 2012 Mathomatic User Guide Table of Contents 1 Introduction and Features History Developer Information 2 3 4 5 Equations and Expressions a Equations b Non Equations c Constants d Variables e Operators 1 Order of Operations example f Complex Numbers 6 Commands 7 Documentation License Mathomatic Command Reference Introduction and Features Mathomatic is an easy to use and colorful algebra calculator that can symbolically e combine and solve equations containing many variables e completely simplify and compare mathematical expressions and equations e do simple calculus transformations and series sum 1 and product e perform generalized real number complex number modular and polynomial arithmetic e generate efficient C Java or Python language code from simplified equations e plot expressions with gnuplot in two or three dimensions etc The name Mathomatic is a portmanteau of math and automatic It is a unique computer algebra system CAS in that all constants are one or more floating point values All numeric arithmetic is IEEE standard floating point arithmetic which most computers do very quickly Mathomatic is written entirely in C which is like a CAS written in assembly language running as fast as the computer allows without any high level language over
25. Number and it means an invalid or indeterminate floating point arithmetic result NaN cannot be directly entered into Mathomatic The appearance of the constant NaN in an expression means the expression is unusable Fractions such as 100 101 are preserved if the numerator and denominator are not large Fractions are always presented in fully reduced form for example 6 9 is converted to the irreducible fraction 2 3 Constants which are exactly equal to a fraction are converted and displayed as fully reduced fractions for example 0 5 converts to 1 2 Mathomatic internally converts a fraction to a single floating point value then may convert it back to a fraction for display after all floating point arithmetic has been done if the result is equal to a fraction Irrational numbers such as the square root of two 24 1 2 and pi are preserved and simplified for exactness unless explicitly approximated Denominators of fractions are usually rationalized in Mathomatic for example 1 2 1 2 becomes the equivalent 2 1 2 2 upon simplification This can be turned off with the command set no rationalize_denominators Constants 7 Mathomatic User Guide 10 23 2012 Variables Variables are what Mathomatic is all about That is where the term symbolic comes from because variables are symbolic in nature They are symbols that can represent known or unknown values or any expression Variables need not be defined in Mathomatic just ente
26. able The simplify command is automatically used on both expressions if needed If this compare command says the equations or expressions are identical then they are definitely identical If this command says the equations or expressions differ then they might be identical if they are too hard for Mathomatic to simplify completely The symbolic option uses the simplify symbolic option when simplifying This option sometimes simplifies more but is not 100 mathematically correct The approximate option runs the approximate command on both expressions or equations This makes the compare command more likely to succeed repeat compare simplifies fully instead of just once making the compare more likely to succeed too Another way of comparing expressions by simply setting them equal is a convenient way of checking validity too with Mathomatic Just solve for any variable to see if it is an identity or typing solve verify 0 works too If it is an identity it will say so meaning both equations sides are mathematically equivalent and identical Copy command Syntax copy select equation number ranges This command simply duplicates the current or specified equation spaces The new duplicated expressions are stored in the next available equation spaces and displayed along with their new equation numbers If the select option is given make the current equation the first expression created by this copy command other
27. ables are supplied with constant values then each solution will be a constant otherwise the result will contain the variables you didn t enter values for Nothing is modified by this command This command is used to temporarily plug in values and approximate simplify expressions and expand sign variables When an expression with only numbers is entered at the main prompt this calculate command is automatically invoked on it autocalc displaying the calculated result This occurs only when set autocalc is on which it is by default If there are any simple numerical fractions in the result those are displayed alongside any short result To only simplify and expand sign variables in stored expressions without approximating use the simplify sign command instead If a feedback variable and number of iterations are specified on the calculate command line you will be prompted for the initial value of the feedback variable and the calculation will be iterated with the simplified Approximate command 18 Mathomatic Command Reference 10 23 2012 result repeatedly plugged back into the feedback variable This will be done until convergence the output equals the input or when the specified number of iterations have been performed if non zero whichever comes first To see all of the intermediate values type set debug 1 before this calculate factor factorizes all integers and variables before display Examples of using the c
28. addressed as you You accept the license if you copy modify or distribute the work in a way requiring permission under copyright law A Modified Version of the Document means any work containing the Document or a portion of it either copied verbatim or with modifications and or translated into another language A Secondary Section is a named appendix or a front matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document s overall subject or to related matters and contains nothing that could fall directly within that overall subject Thus if the Document is in part a textbook of mathematics a Secondary Section may not explain any mathematics The relationship could be a matter of historical connection with the subject or with related matters or of legal commercial philosophical ethical or political position regarding them GNU Free Documentation License 53 GNU Free Documentation License 10 23 2012 The Invariant Sections are certain Secondary Sections whose titles are designated as being those of Invariant Sections in the notice that says that the Document is released under this License If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant The Document may contain zero Invariant Sections If the Document does not identify any Invariant Sections then there are none The Cover Texts are
29. age code The default is C double precision floating point code The output from this command should compile correctly and emulate the equation from Mathomatic if no warnings are given With code integer integer arithmetic is assumed otherwise double precision floating point arithmetic is assumed code integer is more generic and should work with any language To represent factorials the user supplied function factorial is called since there is no equivalent function or operator in these languages factorial functions for several languages are supplied in the directory examples in the Mathomatic source distribution For the most efficient code use the simplify and optimize commands on your equations before running this code command The C and Java languages require that all variables be defined before use The variables command is provided for this The output of the variables command should be put before the output of the code command when compiling Clear command 20 Mathomatic Command Reference 10 23 2012 Compare command Syntax compare symbolic approximate equation number with equation number This command compares two equation spaces to see if they are mathematically the same equal If only one equation number is supplied the comparison is between the current equation and the specified equation The comparison will be faster and more accurate if both equations are previously solved for the same vari
30. alculate There are 2 solutions Solution number 1 with sign 1 x 0 Solution number 2 with sign 1 x 1 LS Solving Equations 16 Mathomatic Command Reference 10 23 2012 A manual solve operation can be done too for educational purposes To apply an expression to both sides of an equation just type the operator followed by then the expression to apply For example 1 gt a b c We want to solve this simple equation manually for c b l a s c 1 gt c Multiply both equation sides by c l a c b 1 gt a Divide both sides by a now manually solved for c The above syntax works for non equations too To see all of the steps performed during an automated solve operation type set debug 1 or set debug 2 for more details before solving 1 gt x at1 b 2 1 x a 1 b 2 1 gt set debug 1 Success 1 gt b Solve for variable b level 1 x a 1 b 2 Subtracting a 1 b 2 from both sides of the equation level 1 x a 1 b 2 0 Subtracting x from both sides of the equation level 1 1 a 1 b 2 1 x Dividing both sides of the equation by 1 level 1 a 1 b 2 x Dividing both sides of the equation by a 1 level 1 b 2 x a 1 Subtracting 2 from both sides of the equation level 1 b x a 1 2 Solve completed level 1 b x a 1 2 Solve successful
31. alculate command 1 gt y x 2 x 1 y x 2 x 1 gt x solve for x Equation is a degree 2 polynomial in x Equation was quadratic 1 1 1 1 4 y sign 2 1 x 2 1 gt calculate Enter y 0 There are 2 solutions Solution number 1 with sign 1 x 1 Solution number 2 with sign 1 x 0 1 gt An example of iteration 1 gt x_new x_old y x_old 2 iterative formula for calculating the square root of y 2 x_new 2 gt calculate x_old 1000 iterate up to 1000 times to calculate the square root of 100 Enter y 100 Enter initial x_old 1 Convergence reached after 9 iterations x_new 10 2 gt Calculate command 19 Mathomatic Command Reference 10 23 2012 Note that the Mathomatic Symbolic Math Library does not support use of the calculate command at this time Clear command Syntax clear equation number ranges This command clears the specified equation spaces so that they are empty and can be reused They are deleted from RAM only clear all quickly clears all equation spaces and restarts Mathomatic resetting internal memory and deleting all expressions stored in RAM without losing your settings Code command Syntax code c or java or python or integer equation number ranges This command outputs the current or specified equations as floating point or integer assignment statements in C Java or Python programming langu
32. athomatic with color mode disabled unless the e or b option is given Use set color 0 to display normal text as all green as it was for many years The default for normal text is no color but if color is followed by a number the normal text color is set to that number set bold enables highlighting in color mode It makes all output brighter Use this if any colors are difficult to see The b option also sets this and color mode on set html same as the x option enables HTML mode for all standard output set html all enables HTML mode for all output even redirected output HTML mode is very useful by itself or with color mode With color mode ANSI color will be turned off and HTML color will be turned on Even bold colors makes a difference here allowing easier viewing on a dim background set alternative same as the a option switches color mode to its alternative color mode if any So far only the MinGW version uses this option for switching to ANSI color mode when using Cygwin set columns followed by a positive integer sets the expected number of character columns width on a terminal screen with line wrap When an expression is to be displayed in multi line fraction format two dimensional and it is wider than this number of screen columns single line format is used instead because otherwise the expression would not display properly due to wrap around set no columns or set columns 0 does no checking for
33. aults to your home directory This command can be shortened to set dir Simplify command Syntax simplify sign symbolic quick est fraction equation number ranges This command fully simplifies reduces expressions in selected equation spaces The result is usually the smallest possible easily readable expression that is mathematically equivalent to the original expression Simplify command 46 Mathomatic Command Reference 10 23 2012 Use this command whenever you think an expression is not completely simplified or if you don t like the way an expression is factored Sometimes simplifying more than once or using the symbolic option simplifies even more This command always tries to factor polynomials if it will make the expression smaller unless the quickest option is given More than one option may be specified at a time Options simplify sign conveniently expands all sign variables by substituting them with all possible combinations of values 1 and 1 storing the unique results into new equation spaces and simplifying This will effectively create one simplified equation for each solution The symbolic option indicates a n m should always be reduced to a n m This often simplifies more and removes any absolute value operations a 2 5 a4 2 5 a 1 a Try this symbolic option if the simplify command doesn t simplify well it often helps with powers raised to powers though it is so
34. ave it before quitting Roots command 42 Mathomatic Command Reference 10 23 2012 Set command Syntax set no option value This command sets various options listed below for the current session They remain in effect until you exit Mathomatic Typing set without arguments shows all current option settings The specified option is turned on unless it is preceded by no which turns it off Some options can be followed by a number and some options can be followed by text setting that option to the following value To permanently change the default settings of Mathomatic set options can be put in the file mathomaticrc for Microsoft Windows mathomatic rc in the same directory as the Mathomatic executable or in the HOME directory It should be a text file with one or more set options per line That file is loaded every time Mathomatic starts up when not in test demo or high security mode The command set save conveniently saves all current session options in that file making them permanent set no save removes that file so then Mathomatic will start up with all options set to the program defaults set save string saves only the specified literal ASCII string in that file for only permanently setting a few options without using your text editor Each set save command overwrites the previously saved settings set load loads the startup set options file once again displaying each line before it is proces
35. bed below in alphabetical order If the command name is longer than 4 letters you only need to type in the first 4 letters for Mathomatic to recognize the command Option words and arguments for commands follow the command name and are separated by spaces Commands are not executed until you press the Enter key and any missing command line arguments that don t have a default are prompted for For example the Mathomatic command help calculate gives short help and usage information for the calculate command help is the command calculate is the argument which is also a command in this case Many commands have an optional equation number range argument which specifies the equation spaces that the command is to operate on An equation number range may be a single equation number or a range of equation numbers separated by a dash like 2 7 which means every equation space between and including equations 2 and 7 or the word all which specifies all equation spaces If omitted or a dash by itself is entered the current expression or equation is assumed If pluralized as equation number ranges in the command syntax that means multiple equation numbers and ranges may be specified for that command separated by spaces A greater than character gt may be appended to the end of any command line followed by a file name This will redirect the output of the command to that file If the file already exists it will be overwritten
36. ble a to check the answer Raising both sides to the power of 2 and unfactoring b 2 1 1 gt simplify 1 1 a b b Solving Equations 15 Mathomatic Command Reference 10 23 2012 1 gt You can prefix the solve variable name with to solve and swap equation sides putting the solve variable on the Right Hand Side Typing by itself will only swap sides of the current equation and display If the current expression is a non equation then prefixing or suffixing an expression with will add that expression as the other equation side conveniently making it an equation you can solve 1 gt x 2 x Entering a simple quadratic polynomial non equation 1 x 2 x 1 gt 0 Setting it equal to zero as an afterthought Combining to make an equation out of the current non equation 1 0 x 2 x 1 gt 0 Current equation is an equation now so zero solve flipping sides Solve successful 1 x x 1 0 1 gt 0 Solve for 0 again flipping equation sides Don t need with autosolve Solve successful 1 0 x x 1 1 gt unfactor Expand to show nothing has changed 12 SRS ate OK 1 gt Demonstrating by itself Swapping both sides of the current equation 1 x 2 x 0 1 gt x Solve for variable x Equation is a degree 2 polynomial equation in x Equation was solved with the quadratic formula Solve successful 1 gt c
37. blicense or distribute the Document except as expressly provided under this License Any attempt otherwise to copy modify sublicense or distribute it is void and will automatically terminate your rights under this License However if you cease all violation of this License then your license from a particular copyright holder is reinstated a provisionally unless and until the copyright holder explicitly and finally terminates your license and b permanently if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation Moreover your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means this is the first time you have received notice of violation of this License for any work from that copyright holder and you cure the violation prior to 30 days after your receipt of the notice Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License If your rights have been terminated and not permanently reinstated receipt of a copy of some or all of the same material does not give you any rights to use it 10 FUTURE REVISIONS OF THIS LICENSE The Free Software Foundation may publish new revised versions of the GNU Free Documentation License from time to time Such new versions will be similar in spiri
38. ccurate from 12 to 14 digits due to accumulated round off error because all constants are stored internally as double precision rounded to 15 decimal digits floats And the amount of round off error is not tracked making Mathomatic unsuitable for applications requiring high precision like astronomical calculations Excepting constants with a name like inf for the infinity constant constants always start with a decimal digit 0 9 a period or a dash Examples of equivalent constants follow Normal Notation base 10 Scientific Notation base 10 Hexadecimal Notation base 16 Expressions that are not equations 6 Mathomatic User Guide 10 23 2012 The exact syntax to enter constants as above may be found by looking up the C library function st rtod 3 In the Unix shell man strtod will do that Double precision floating point limits e The largest valid constant is 1 797693e 308 slightly less than 2 1024 e The smallest valid constant is 2 225074e 308 or 0 The infinity constant is entered by typing inf Positive and negative infinity are distinct and understood however division by zero produces one infinity value not the two valued infinity which would be more correct Also floating point overflow produces either positive or negative infinity 1 gt 1 0 Warning Division by zero answer inf 1 gt 0 0 Warning Division by zero answer nan i gt nan or NaN stands for Not a
39. cense 10 23 2012 If the Cover Text requirement of section 3 is applicable to these copies of the Document then if the Document is less than one half of the entire aggregate the Document s Cover Texts may be placed on covers that bracket the Document within the aggregate or the electronic equivalent of covers if the Document is in electronic form Otherwise they must appear on printed covers that bracket the whole aggregate 8 TRANSLATION Translation is considered a kind of modification so you may distribute translations of the Document under the terms of section 4 Replacing Invariant Sections with translations requires special permission from their copyright holders but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections You may include a translation of this License and all the license notices in the Document and any Warranty Disclaimers provided that you also include the original English version of this License and the original versions of those notices and disclaimers In case of a disagreement between the translation and the original version of this License or a notice or disclaimer the original version will prevail If a section in the Document is Entitled Acknowledgements Dedications or History the requirement section 4 to Preserve its Title section 1 will typically require changing the actual title 9 TERMINATION You may not copy modify su
40. comes the current equation Any previously entered expression can be automatically entered again by entering a followed by the relative or absolute equation space number of that expression If this is entered first thing at the main prompt it means something entirely different that you are selecting that equation space Otherwise the RHS or expression at that equation space is substituted for your convenience Equations To enter an equation into the first available equation space and make it the current equation simply type or copy paste it in at the main prompt Each equation space consists of two equation sides called the Left Hand Side LHS and the Right Hand Side RHS separated by an equals sign Each equation side consists of a mathematical expression which is a mix of constants variables and operators mostly in standard algebraic infix notation Parentheses are used to override operator precedence and group things together Valid parentheses characters are and are reserved for array subscripts in variable names Note that the equals sign does not make an assignment to any variables it only signifies equality sameness between the results of evaluating the LHS and RHS Shown here is a valid equation with its parts labeled Startup 4 Mathomatic User Guide 10 23 2012 equation variables constant l a b c 2 l l l l E operators LHS RHS In the above equati
41. e gnuplot command line enter set debug 1 beforehand to set debug level 1 for the current session Optimize command 37 Mathomatic Command Reference 10 23 2012 Plots may be customized Typing set plot_prefix at the Mathomatic main prompt followed by a string of 8 bit characters will prepend the string to the gnuplot plot string when using the Mathomatic plot command For example if you type set plot set polar at the Mathomatic main prompt 2D polar plots will be performed instead with subsequent plot commands using variable t instead of x Product command Syntax product variable start end step size Alternate syntax product variable start to end step step size This command performs a mathematical product of the current expression or the RHS of the current equation as the index variable goes from start to end in steps of step size default 1 The result is approximated simplified stored and displayed The current equation is not changed 1 gt y a x 1 y a x 1 gt product Enter variable x x 1 To 10 2 y 3628800 a 10 1 gt 10 Answer 3628800 1 gt To see all of the intermediate results type set debug 1 before this Push command Syntax push equation number ranges or text to push This command pushes the current or specified equation spaces into the readline history for easy editing and re entry by using the cursor keys The equation spaces are not
42. eatedly prompt for integers to factorize until an empty line is given Multiple integers integer ranges two integers separated with a dash or multiple expressions that evaluate to integers can be specified on the same line and should be separated with spaces or commas Without the number option this command will factor out repeated sub expressions and repeated integer factors the GCDs in equation spaces When factoring expressions this command does some basic simplification and factors out any common mathematically equal sub expressions it can unless variables are specified on the command line in which case only common sub expressions containing those variables are factored out This collects together terms involving those variables For example with the following expression b c b d variable b factors out and the result of this command is b c d If no variables are specified on the command line this command factors even more the bases of common mathematically equal bases raised to any power are factored out This is called Horner factoring or Horner s rule For example 1 gt 2 3x 2 x y 1 2 3 x 2 x y 1 gt unfactor expand 1 4 x 12 x 2 9 x 3 4 y 12 x y 9 x 2 y 1 gt factor x collect terms containing x 1 x 4 12 y x 2 12 9 y 9 x 3 4 y 1 gt x 3 2x 2 3x 4 enter another expression 2 x 3
43. ent under the conditions of sections 2 and 3 above provided that you release the Modified Version under precisely this License with the Modified Version filling the role of the Document thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it In addition you must do these things in the Modified Version e A Use in the Title Page and on the covers if any a title distinct from that of the Document and 2 VERBATIM COPYING 55 GNU Free Documentation License 10 23 2012 from those of previous versions which should if there were any be listed in the History section of the Document You may use the same title as a previous version if the original publisher of that version gives permission e B List on the Title Page as authors one or more persons or entities responsible for authorship of the modifications in the Modified Version together with at least five of the principal authors of the Document all of its principal authors if it has fewer than five unless they release you from this requirement e C State on the Title page the name of the publisher of the Modified Version as the publisher e D Preserve all the copyright notices of the Document e E Add an appropriate copyright notice for your modifications adjacent to the other copyright notices e F Include immediately after the copyright notices a license notice giving the public permission to use the Modified Version under
44. entury Mathomatic was ported to the GNU C Compiler gcc under Linux and became free and open source software by publishing under the GNU Lesser General Public License LGPL version 2 1 The graphing program was discontinued 2D 3D graphing of equations is now accomplished with gnuplot Mathomatic is currently developed and maintained on a Linux x86 64 bit computer and now stands at 23 000 lines of code including comments It has been optimized for speed by using Linux debugging utilities that tell where Mathomatic spends most of its time Developer Information Building Mathomatic from source requires a C compiler with the standard C libraries If compiled with the GCC C compiler or the Tiny C Compiler for a Unix like operating system no changes need to be made to the source code See the file README txt for compilation instructions Mathomatic uses no special GCC only code so it will usually compile easily with any C compiler Mathomatic can easily be ported to any computer with at least 1 megabyte of free RAM In the standard distribution found on the Mathomatic home page the maximum memory usage defaults to 400 megabytes the version status command tells this Maximum memory usage is not reached unless all equation spaces are filled The default maximum memory usage should be less than the amount of free RAM and can be easily reduced by compiling with the DHANDHELD compiler command line option which reduces the memory requirements t
45. es only power operator expansion that is a b n m is transformed to a4n a4m b 4n b4m Variables command woe motte java integer m Syntax variables c count equation number ranges Show or define all variable names used within the specified expressions from most frequent to least frequently occurring The programming language options output the variable definitions required to make code from the specified equations This does not initialize any variables it only defines them as needed for a C or Java compiler This command is not necessary for generating Python code The count option displays the total counts of each variable in a comment for the specified expressions The count means the number of times the variable occurs This command returns false with failure and an error message if no variables were found This may be useful for determining whether an expression is numeric or symbolic Unfactor command 51 Mathomatic Command Reference 10 23 2012 Version command Syntax version status Shows the version number of Mathomatic If the status option is given also displays the last main prompt return value the C compile time definitions used and other useful C compiler information the expression array size the maximum possible memory usage the invoked security level and readline status for the currently running version of Mathomatic The maximum memory usage displayed is the am
46. esult of solving for a variable by plugging all solutions into the original equation and then simplifying and comparing If the resulting equation sides are identical an identity a Solutions verified message is displayed meaning that all of the solutions are correct Otherwise Solution may be incorrect is displayed meaning at least one of the solutions is incorrect or unverifiable causing the verifiable option to return with failure and the verify option to return with 2 Use the verifiable option if verification is required otherwise use the verify option The verify options work when solving for a single variable and indicate if the solve result can be trusted If the verify options are used when solving for zero they only check if the result of the zero solve is an identity The simplify quick command is automatically used after every successful solve operation when using the verify options The for option has no additional effect and is to make entering this solve command more natural Sum command Syntax sum variable start end step size Alternate syntax sum variable start to end step step size This command performs a mathematical summation of the current expression or the RHS of the current equation as the index variable goes from start to end in steps of step size default 1 The result is approximated simplified stored and displayed The current equation is not changed 1 gt y a x S
47. h integer and constants and no non integer division Modulus simplification with integer variables and expressions will almost always simplify more than with normal variables and non integer expressions Most modulus simplification is done by the simplify command only set fixed_point sets finance fixed point or integer display Finance mode set with no arguments or an argument of 2 displays all constants with 2 digits after the decimal point for example 2 00 and negative numbers are always parenthesized for example 2 00 Displayed constants are rounded to the nearest cent though internally there is no loss of accuracy until more than 15 digits have been used The number of digits to display Options 45 Mathomatic Command Reference 10 23 2012 after the decimal point may be specified with set fixed_point number This is not truly fixed point arithmetic it is floating point displayed as fixed point With double precision floating point only the most significant 15 decimal digits will ever be correct set fixed_point 0 sets rounded integer only output with no decimal points this might be useful for something The default is floating point display and no fixed point display set no fixed_point set factor_integers sets automatic factoring of integers for all displayed expressions When set all integers of up to 15 decimal digits are factorized into their prime factors before the result of any command is di
48. he polynomial GCD is used when reducing algebraic fractions factoring polynomials and for simplifying The Euclidean GCD algorithm of successive divides is the best way to compute the GCD for numbers and polynomials Multivariate polynomial GCD computation usually requires recursion of the GCD algorithm or other methods Currently the polynomial GCD routine in Mathomatic is not recursive making it univariate and simpler Because it is univariate Mathomatic might be unable to find the GCD of polynomials with many variables Finding the GCD of large polynomials will probably not succeed anyways with floating point arithmetic because of accumulated round off error The polynomial division algorithm in Mathomatic is generalized and able to handle any number of variables multivariate and division is always done with one selected base variable to be proper polynomial division Being generalized the coefficients of the polynomials may be any mathematical expression not containing the base variable An example of polynomial division 1 gt divide Enter dividend x 4 7 x 3 18 x 2 22 x 12 Enter divisor x 2 2 x 2 Polynomial division successful using variable x The quotient is 6 F 72 57x The remainder is 0 Polynomial Greatest Common Divisor iterations 1 x 2 2 x 2 i gt Divide command 24 Mathomatic Command Reference 10 23 2012 The number of iterations displayed i
49. he specified variables in the current equation with the RHS of solved equations The equation to solve can be specified with the using argument If using is not specified Mathomatic will search backwards starting at the current equation minus one for the first equation that contains the specified variable The equation to solve is solved for the specified variable then the RHS is inserted at every occurrence of the specified variable in the current equation That effectively eliminates the specified variable from the current equation resulting in one less unknown There is an advantage to eliminating multiple variables in one command each equation will be used only once If the same equation is solved and substituted into the current equation more than once it will cancel out eliminate all is shorthand for specifying all normal variables on the command line repeat eliminate all will eliminate all variables repeatedly until nothing more can be substituted using each equation only once Here is a simple example of combining two equations 1 gt This arrives at the distance between two points in 3D space from the 1 gt Pythagorean theorem distance between two points on a 2D plane 1 gt The coordinate of point 1 2D xl yl 3D xl yl zl 1 gt The coordinate of point 2 2D x2 y2 3D x2 y2 22 gt 1 gt L 2 x1 x2 2 yl y2 2 Distance formula for a 2D Cartesian plane 1 L42
50. head Mathomatic is exceptionally good at solving differentiating simplifying calculating and visualizing elementary algebra It is a console mode application using a color command line interface CLI with Mathomatic User Guide 1 Mathomatic User Guide 10 23 2012 pretty print output that runs in a terminal emulator under any operating system The console interface is very simple and requires little more than learning the basic algebra notation to get started a Mathomatic user says joyfully on Wikipedia All input and output is line at a time ASCII text By default input is standard input and output is standard output Mathomatic can be compiled with editline or GNU readline for easier line input The pretty print output is even prettier in HTML output mode which supports color too History Mathomatic has been developed and supported almost every day by George Gesslein II with help from the Internet community Mathomatic development started in the year 1986 to test new ideas and as an experiment in computerized mathematics originally using the Microsoft C compiler for DOS and the author s own text editor as the only development tools Versions 1 and 2 were published by Dynacomp of Rochester New York in 1987 and 1988 as a scientific software product for DOS Afterwards it was released as shareware and then emailware with a 2D equation graphing program that could find asymptotes written in Microsoft C for DOS At the turn of the c
51. iation command is not needed Some examples 1 gt x 34 x 24 x4 1 de 183 892 x 1 1 gt derivative no need to specify the variable if there is only one Differentiating with respect to x and simplifying 2 3 x 2 2 x 1 2 gt a x n 3 a x n show a general rule of differentiation 3 gt derivative x Differentiating with respect to x and simplifying 4 a n x n 1 4 gt integrate x undo the differentiation 5 a x n 5 gt Derivative command 22 Mathomatic Command Reference 10 23 2012 Display command Syntax display factor simple or mixed equation number ranges This command displays stored expressions in nice looking multi line 2D two dimensional fraction format where division is displayed as a numerator over a fractional line made up of dashes over a denominator If the width number of columns required for this 2D display exceeds the screen width the expression is displayed instead in single line one dimensional format by the list command The screen width is set automatically on startup or by the set columns option Non integer constants are converted to reduced fractions if they are exactly equal to a simple fraction and it would improve readability The factor option causes all integers less than or equal to 15 decimal digits long to be factorized into their prime factors before display including the numerator and denominat
52. ision and polynomial division are tried on any algebraic divides possibly making complex fractions if it reduces the expression size Lastly the expressions are nicely factored and displayed Smart division is a symbolic division like polynomial division but it tries every term in the dividend instead of only the term with the base variable raised to the highest power to make the expression smaller repeat simplify repeatedly runs the simplify command until the result stabilizes to the smallest size expression In other computer algebra systems this is called full simplification Options 47 Mathomatic Command Reference 10 23 2012 Solve command Syntax solve verify or verifiable equation number range for expression This command automatically solves the specified equations for the specified expression which may be a variable or zero For each successful solve operation the equation solved is replaced with the solution becomes the current equation and is displayed See the section on Solving Equations for more information on solving with Mathomatic Solving for variable 2 or 0 2 will isolate the square root of the largest expression containing the specified variable and then square both sides of the equation This is a new feature for properly squaring cubing etc both sides of an equation and it works for any power and variable with any equation with roots The verify and verifiable options check the r
53. lon character If any command in the text file prompts for input it will not read the input from the text file instead it will prompt the user for the input Expressions saved with the save command are restored using this read command This command is automatically executed when you start up Mathomatic with file names on the shell command line The file name may be a directory name in which case the current directory is changed to that directory The default file name extension suffix for Mathomatic input files is in A file name extension is not required This command may be preceded with repeat which repeatedly reads a script until it fails or is aborted Push command 39 Mathomatic Command Reference 10 23 2012 Without any arguments this command does an Is C command in Unix Linux or dir W P under MS Windows listing the current directory contents Real command Syntax real variable This command copies the real part of a complex number expression to the next available equation space First it fully expands the current equation space with imaginary number simplification Then if the current expression or RHS of the current equation is not complex the warning message Expression is not a mix will be displayed A complex number expression contains both imaginary and real number parts To copy only the imaginary number part see the imaginary command The separation variable may be specified on the com
54. mand line the default is the imaginary unit i There will be no imaginary numbers in the result 1 gt atb i ct d i a b i I essen c d i gt real a c b d 2 c 2 d 2 2 gt Repeat command Syntax repeat command arguments Any command may be preceded by repeat which sets the repeat flag for that command Many commands ignore the repeat flag if repeating them doesn t make sense Sometimes repeating means do a full simplify when simplifying for example in the simplify compare derivative extrema and taylor commands etc Currently the approximate calculate compare derivative divide echo eliminate extrema fraction read Read command 40 Mathomatic Command Reference 10 23 2012 replace roots simplify and taylor commands all use the repeat flag Replace command Syntax replace variables with expression By default this command prompts you for a replacement expression for each variable in the current expression or equation If an empty line is entered for a variable that variable remains unchanged The result is placed in the current expression or equation and displayed This command is very useful for renaming or substituting variables It is smart enough to do variable interchange With the handy repeat option you are repeatedly prompted for values of the variables the result is simplified checked for being an identity and displayed Nothing i
55. matic format The text result can then be entered or read back into Mathomatic Formatting options list export outputs expressions in a generally exportable single line text format You can cut and paste the expressions or redirect them to a file so they can be read in with a different math program list maxima is for making expression output compatible with the free computer algebra system Maxima list gnuplot is for making expression output that is compatible with the free graphing utility gnuplot list hex displays as normal without these options except constants are displayed as hexadecimal values in binary exponential notation where no precision is lost by display rounding Display rounding of constants happens only to the displayed value not the stored value and only if a floating point value is converted to decimal for display so just displaying decimal constants does not ever change their value internally unless they are read back in Expressions that are displayed by this hex option have done no display rounding and can be read back into Mathomatic exactly as they were But the hex format used here is very ugly and not the hexadecimal you would expect due to the binary exponent The standard C math Limit command 34 Mathomatic Command Reference 10 23 2012 libraries provide no better hexadecimal or other base output They were meant for decimal display only list primes runs the matho primes utility
56. metimes not 100 mathematically correct The quick option skips expanding sums raised to the power of 2 or higher like x 1 45 Also algebraic fractions might be simpler with this option and unlike denominators are not combined at all This option often simplifies the best unless expanding sums raised to an integer power is needed The quickest option very basically simplifies without any unfactoring nor factoring Running the simplify command with this option makes it complete almost instantaneously simplify fraction usually simplifies any expression with division in it down to the ratio of two polynomials or expressions like Maxima s rat simp function does though sometimes the fraction command works better because it always reduces to a simple fraction the difference here being the simplify command result will be completely simplified This is accomplished by simplification without doing unfactor fraction and without doing polynomial or smart algebraic division on the divide operators This simplify command applies many algebraic transformations and their inverses for example unfactor and then factor and then tries to combine and reduce algebraic fractions and rationalize their denominators Complex fractions are converted to simple fractions by making the denominators of fractions added together the same combining and simplifying Polynomials with repeated or symbolic factors are factored next Then smart heuristic div
57. mple fractions for example 9 4 is displayed as 2 1 4 which is a mixed fraction also called a mixed number set no prompt turns off Mathomatic prompt output exactly like the q quiet mode option does set rationalize will set the rationalize_denominators option which attempts to move radicals from the denominator of fractions to the numerator during simplification This is the default set modulus_mode should be followed by an integer from 0 to 2 or a language name C Java Python or positive When a modulus operation is done on two constants dividend divisor mode 0 is a type of remainder modulus that returns a result that is the same sign as the dividend same as C and Java s operator give mode 1 returns a result that is the same sign as the divisor same as Python s operator gives and mode 2 returns an always positive or zero result Mode 2 is the default and is 100 mathematically correct and the type of modulus operation that can be generally simplified always and be correct Other types modes of modulus operations will be simplified the same way and the result will be correct as long as they remain positive or zero Setting the modulus mode only affects modulus operator numeric calculations All modulus simplification rules are enabled regardless of the modulus mode Modulus simplification for integer modulus expressions is always accomplished by using integer variables variable names that start wit
58. n example of imaginary numbers being produced 2 5 will be converted to 2 5 i Roots of complex numbers such as i 5 and 5 i will be approximated and only a single root will be produced even though there may be many roots see the roots command That single root is called the principal value which may be unexpected and will often be inexact Because 1 i correctly simplifies to i after significant manipulation different numerical results might be produced with complex numbers and division This is normal so the sooner the result of a complex expression is calculated the better Conjugation of all complex numbers in the current equation is accomplished by typing the following command replace i with i Commands Complex Numbers 10 Mathomatic User Guide 10 23 2012 Mathomatic has about 43 simple English commands that may be typed at the main prompt Please consult the Mathomatic Command Reference for detailed information on all commands Documentation License GNU FDL FREE DOC LICENSE Mathomatic documentation copyright 1987 2012 George Gesslein II Permission is granted to copy distribute and or modify this document under the terms of the GNU Free Documentation License Version 1 3 or any later version published by the Free Software Foundation with no Invariant Sections no Front Cover Texts and no Back Cover Texts A copy of the license is included here in the Mathomatic documentation directory Up to
59. n is needed try the simplify fraction command instead though the result is not always a single simple fraction with the simplify command Help command Syntax help topics or command names Alternate command name This command is provided as a quick reference while running Mathomatic If the argument is a command name a one line description and one line syntax usage info of that command are displayed possibly followed by one more line of additional information about that command Command names and topics may be abbreviated for example help r will display all commands that start with the letter r Entering this command by itself will display a list of available topics and commands help license will display the copyright and license notice for the currently running version of Mathomatic To create a quick reference text file of all Mathomatic commands type help all gt quickref txt Fraction command 30 Mathomatic Command Reference 10 23 2012 Imaginary command Syntax imaginary variable This command copies the imaginary part of a complex number expression to the next available equation space First it fully expands the current equation space with imaginary number simplification Then if the current expression or RHS of the current equation is not complex the warning message Expression is not a mix will be displayed A complex number expression contains both imaginary and real number parts To copy only
60. nuplot expressions This command automatically plots multiple solved mathematical equations or expressions in 2D or 3D with the free graphing utility gnuplot The specified equation spaces are plotted at once along with any comma separated gnuplot expressions on the command line Each expression should contain the variable x to be successfully plotted If it also contains the variable y a 3D surface plot is performed in Cartesian space with the x y and z axes projected on your 2D display z in a 3D plot or y in a 2D plot are the variables the plot expressions are supposedly solved for though they need not be included A gnuplot X range Y range and even a Z range may be specified on the plot command line For example plot 128 128 will make the X axis go from 128 to 128 and plot 128 128 1 1 will also make the Y axis go from 1 to 1 A pair of straight brackets must surround each range Plotting of an equation space with the imaginary number i in it is allowed however plots are always plotted on real Cartesian space showing only real number points If there are no real number points the plot will fail The imaginary unit i is not understood by gnuplot Gnuplot must be installed and accessible from shell by typing gnuplot for this command to work All functions and operators of gnuplot can be used in the gnuplot expressions If gnuplot fails the gnuplot command line is displayed to show what failed To always show th
61. o 1 6th of the default size Memory usage can also be dynamically changed at startup with the m option Introduction and Features 2 Mathomatic User Guide 10 23 2012 The Mathomatic source code can also be compiled as a symbolic math library that is callable from any C compatible program and is mostly operating system independent See the file ib README txt for more developer information and how to include Mathomatic in your free software or proprietary program Very little disk space a few megabytes is required to compile install and run the Mathomatic application A readline library must be installed to compile in and use readline capabilities which allows editing and history recall of all Mathomatic line input by pressing the cursor keys We use editline instead of GNU readline which is in a free Linux package called libeditline dev It is more compact and license compatible than GNU readline Startup SYNOPSIS mathomatic options input_files or input rmath input_files To start the compiled interactive Mathomatic application run a terminal emulator which opens a shell window and type mathomatic at the shell prompt without double quotes If m4 macro Mathomatic was installed you may type rmath instead to use Mathomatic with input of functions like sin x and sqrt x allowed and automatically expanded to equivalent algebraic expressions Logarithm function input is currently not available because
62. o assure everyone the effective freedom to copy and redistribute it with or without modifying it either commercially or noncommercially Secondarily this License preserves for the author and publisher a way to get credit for their work while not being considered responsible for modifications made by others This License is a kind of copyleft which means that derivative works of the document must themselves be free in the same sense It complements the GNU General Public License which is a copyleft license designed for free software We have designed this License in order to use it for manuals for free software because free software needs free documentation a free program should come with manuals providing the same freedoms that the software does But this License is not limited to software manuals it can be used for any textual work regardless of subject matter or whether it is published as a printed book We recommend this License principally for works whose purpose is instruction or reference 1 APPLICABILITY AND DEFINITIONS This License applies to any manual or other work in any medium that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License Such a notice grants a world wide royalty free license unlimited in duration to use that work under the conditions stated herein The Document below refers to any such manual or work Any member of the public is a licensee and is
63. olve command 48 Mathomatic Command Reference 10 23 2012 1 gt sum Enter variable x x 1 To 10 2 y 55 a gt To see all of the intermediate results type set debug 1 before this Tally command Syntax tally average equation number ranges This command prompts for a value adds it to a running grand total approximates simplifies and displays the running total and optional average and repeats The average is the arithmetic mean that is the running total divided by the number of entries count When finished the ending total is returned in the next available equation space displayed and made the current equation It is aconvenient way of adding subtracting and averaging many numbers and or variables Enter a minus sign before each value you wish to subtract Enter an empty line to end The grand total may be set at the start by specifying equation spaces on the command line to add the expressions or Right Hand Sides contained therein together Type tally to resume where you left off last time if the current equation hasn t changed This works because the final result of the last tally session is saved in the next available equation space and made the current equation Taylor command Syntax taylor nosimplify variable order point This command computes the Taylor series expansion of the current expression or RHS of the current equation with respect to the specified variable The
64. on the variable a is called the dependent variable because its value depends on the independent variables b and c In Mathomatic any variable can be made the dependent variable by simply typing the variable name in at the prompt This will solve the current equation for that variable and if successful make that variable the LHS Here is the above equation entered into Mathomatic and solved for b then calculated for the values a 1 and c 1 1 gt a b c 2 I a b c 2 1 gt b 1 b 2 cta 1 gt calculate Enter a 1 Enter c 1 The 1 listed in front of each displayed equation always indicates the equation space number it is stored in Mathomatic automatically does both symbolic and numeric mathematics computations during any manipulations This means that it can handle algebraic formulas as well as numbers What follows is a simple example of the result of both types of computations working together during equation simplification and solving 1 gt 3 x 1 1 2x 4 1 1 3 x 1 1 2 x 1 1 gt simplify 1 8 x 2 2 x 1 1 gt solve verify x Equations 5 Mathomatic User Guide 10 23 2012 Solution verified 1 gt The solve verify command used above solves the current equation and then verifies the result by plugging the result into the original equation and simplifying If an identity results the LHS is identical to the RHS a Solution verified message is displa
65. on successful 2 y 0 16256117185712 1 gt This example avoids the singularity at x 1 and is accurate to 12 digits Optimize command Syntax optimize equation number range This command splits the specified equations into smaller more efficient equations with no repeated expressions Each repeated sub expression becomes a new equation solved for a temporary variable named temp j Note that the resulting assignment statements may be in the wrong order for inclusion in a computer program with the code command the order and generated code should be visually checked before using The source code statements may need to be manually put in the right order to work properly 1 gt y atbtctd atb c d 1 y a b c d a b c d 1 gt optimize 2 temp satb c d 1 y temp temp 1 gt eliminate temp undo the optimization Solving equation 2 for temp Nintegrate command 36 Mathomatic Command Reference 10 23 2012 1 y atb tc d atb tcHd Pause command Syntax pause text This command waits for the user to press the Enter key It is useful in text files scripts that are read in to Mathomatic Optionally a one line text message may be displayed Typing quit or exit before pressing the Enter key will fail this command and abort the current script This command is ignored during test and demo modes Plot command Syntax plot equation number ranges xyz ranges g
66. or of fractions To always factorize integers like this before display use the set factor_integers option The mixed option displays mixed fractions when possible A mixed fraction is an expression like 2 1 4 rather than the simple fraction 9 4 To always display mixed fractions use the set fractions mixed option Displaying simple fractions when not the default is possible now too Divide command Syntax divide base variable dividend divisor This command is for conveniently doing and experimenting with polynomial and numerical division and Greatest Common Divisors GCDs It simply prompts for two expressions the dividend and the divisor if not specified on the command line and divides them displaying the result and the GCD If the base variable name and or two expressions are specified on the command line they must be separated by space or comma characters Mathomatic has a powerful general multivariate polynomial division routine and univariate polynomial GCD routines used by the simplify command which this divide command calls without any other processing if two polynomials are entered This command prompts for the dividend the main polynomial and then the divisor what you want to divide the main polynomial by The polynomial quotient remainder and GCD are displayed The power of the highest power term in the dividend must be greater than or equal to the power of the highest power term in the divisor othe
67. ord processors SGML or XML for which the DTD and or processing tools are not generally available and the machine generated HTML PostScript or PDF produced by some word processors for output purposes only The Title Page means for a printed book the title page itself plus such following pages as are needed to hold legibly the material this License requires to appear in the title page For works in formats which do not have any title page as such Title Page means the text near the most prominent appearance of the work s title preceding the beginning of the body of the text The publisher means any person or entity that distributes copies of the Document to the public A section Entitled XYZ means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language Here XYZ stands for a specific section name mentioned below such as Acknowledgements Dedications Endorsements or History To Preserve the Title of such a section when you modify the Document means that it remains a section Entitled XYZ according to this definition The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document These Warranty Disclaimers are considered to be included by reference in this License but only as regards disclaiming warranties any other implication that these Warranty Disclaimers may have i
68. ount of RAM used when all equation spaces have been filled It does not include stack size which varies or executable code size The Unix Linux size command gives all the other sizes when run as size mathomatic like text size which is really code size Adding together all size values will probably give a close approximation of the total amount of free RAM required by Mathomatic Define HANDHELD 1 when compiling to reduce this Documentation License GNU FDL FREE DOC LICENSE Mathomatic documentation copyright 1987 2012 George Gesslein II Permission is granted to copy distribute and or modify this document under the terms of the GNU Free Documentation License Version 1 3 or any later version published by the Free Software Foundation with no Invariant Sections no Front Cover Texts and no Back Cover Texts A copy of the license is included here in the Mathomatic documentation directory Up to the documentation index www mathomatic org Version command 52 GNU Free Documentation License 10 23 2012 GNU Free Documentation License Version 1 3 3 November 2008 Copyright 2000 2001 2002 2007 2008 Free Software Foundation Inc lt http fsf org gt Everyone is permitted to copy and distribute verbatim copies of this license document but changing it is not allowed 0 PREAMBLE The purpose of this License is to make a manual textbook or other functional and useful document free in the sense of freedom t
69. ransform of 1 2 y x 2 gt a x n a general polynomial term 3 a x n 3 gt laplace x 4 4 gt laplace inverse x 5 a x n Limit command Syntax limit variable expression This command takes the limit of the current expression as variable goes to the specified expression The result is always an equation and placed in the next available equation space and displayed L Hopital s rule for taking limits is not used by this command Instead the limit is taken by simplifying solving and substituting This command is experimental and does not know about negative infinity and occasionally gives a wrong answer when dealing with infinities Laplace command 33 Mathomatic Command Reference 10 23 2012 1 gt 2x x 1 2 x ix 1 1 gt limit x inf take the limit as x goes to infinity Solving 2 limit 2 i This command is experimental in that it tests the effectiveness of solving the equation for the limit variable and simplifying replacing the limit variable with the goes to value or expression then solving back for the original solve variable and simplifying List command Syntax list export or maxima or gnuplot or hex or primes equation number ranges This command displays stored expressions in single line one dimensional format A single formatting option may be specified With no option specified expressions are displayed in decimal Matho
70. re the new expression as an equation set equal to zero Mathomatic Command Reference 12 Mathomatic Command Reference 10 23 2012 e A variable to automatically solve the current equation for autosolve e An operator not factorial followed by an equals sign and an expression which is applied to both sides of the current equation or to the current non equation e An equation number to select as the current equation autoselect e A slash or pound sign followed by a variable name to search all equations spaces forward or backward for respectively e A Mathomatic command listed in this document e A question mark followed by a topic for quick short help same as the help command e A semicolon followed by a line comment everything on a line after a semicolon is ignored A semicolon that does not start a line comment may be entered by preceding it with a backslash e An exclamation point followed by a shell or system command by itself invokes the default shell is also the factorial operator If a colon starts the line preceding any of the above input to the main prompt it will always return with successful status preventing any current read command operations from aborting Entering Commands Mathomatic has about 43 commands that may be typed at the main prompt Most commands operate on the current expression or equation by default Commands are simple English words and are descri
71. ring the variable name is enough Variable names consist of any combination of letters a z digits 0 9 and underscores _ They never start with a digit By using the set special_variable_characters command you can add to the allowed variable name characters By default letters in variable names are case sensitive meaning the alphabetic case of each letter in the variable name is important For example variables named A1 and al represent two different variables unless set no case_sensitive is entered beforehand The following variables are predefined and are not normal variables e amp or e the universal constant e 2 718281828 pi or pi the universal constant pi 3 1415926 i 1 or i the imaginary unit square root of 1 sign sign1 sign2 may only be 1 or 1 integer integerl may be any integer value The above can be used anywhere variables are required To automatically enter multiplication by a unique two valued sign variable precede any expression with Operators Mathomatic implements the standard rules of algebra for addition subtraction multiplication division modulus and all forms of exponentiation or An example of a rule of algebra is 2 x 3 x being simplified to 5 x All available operators are at least numerically capable most are symbolically capable too see above paragraph and have precedence decreasing as indicated
72. rwise the polynomial division will fail as it should In other words the degree of the divisor polynomial must be less than or equal to the degree of the dividend polynomial Display command 23 Mathomatic Command Reference 10 23 2012 A base variable name may be specified first on the command line as the base variable of the two polynomials but is usually not necessary because a good base variable is automatically selected that works for the division If two numbers are entered instead of polynomials the result of the numerical division the GCD and the Least Common Multiple LCM are displayed The LCM of two numbers is the smallest positive number that can be evenly divided by both numbers separately without remainder The LCM is the same as the Lowest Common Denominator LCD of two fractions and is the two numbers multiplied together divided by the GCD The Greatest Common Divisor of a and b is defined as the greatest positive number or polynomial that evenly divides both a and b without remainder In Mathomatic the GCD is not necessarily integer unless both a and b are integers The Euclidean GCD algorithm is used by Mathomatic to compute the GCD for numbers and polynomials The GCD is the best way to reduce any fraction to its simplest form Just divide the numerator and denominator by their GCD and replace each of them with their quotients there will be no remainder the result is a completely reduced equivalent fraction T
73. s void and has no effect on the meaning of this License 1 APPLICABILITY AND DEFINITIONS 54 GNU Free Documentation License 10 23 2012 2 VERBATIM COPYING You may copy and distribute the Document in any medium either commercially or noncommercially provided that this License the copyright notices and the license notice saying this License applies to the Document are reproduced in all copies and that you add no other conditions whatsoever to those of this License You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute However you may accept compensation in exchange for copies If you distribute a large enough number of copies you must also follow the conditions in section 3 You may also lend copies under the same conditions stated above and you may publicly display copies 3 COPYING IN QUANTITY If you publish printed copies or copies in media that commonly have printed covers of the Document numbering more than 100 and the Document s license notice requires Cover Texts you must enclose the copies in covers that carry clearly and legibly all these Cover Texts Front Cover Texts on the front cover and Back Cover Texts on the back cover Both covers must also clearly and legibly identify you as the publisher of these copies The front cover must present the full title with all words of the title equally prominent and visible You may add other material on the
74. s changed with the repeat option If variables are specified on the command line you will be prompted for those variables only and all other variables will be left unchanged If with is specified the repeat option is ignored you won t be prompted and all variables specified will be replaced with the expression that follows Roots command Syntax roots root real part imaginary part This command displays all complex number roots of a given positive integer root of a complex number The number of the root equals the number of correct solutions For example 3 would give the 3 roots of the cube root This command will also convert rectangular coordinates to polar coordinates The floating point real part X coordinate and imaginary part Y coordinate of the complex number are prompted for Just enter an empty line if the value is zero The polar coordinates of the given complex number are displayed first which consist of an amplitude distance from the origin and an angle direction Then each root is calculated and displayed along with an Inverse check value if debugging is enabled which should equal the original complex number The Inverse check is calculated by repeated complex number multiplication of the root times itself Since double precision floating point is used the results are only accurate from 10 to 12 decimal digits 1 gt roots Enter root positive integer 3 Enter real part X 8 Enter imaginary part Y
75. s the number of polynomial divides done to compute the GCD with the Euclidean algorithm repeat divide repeatedly prompts for all input performing its function again and again until empty lines are given Echo command Syntax echo text By default this command outputs a line of text followed by a newline repeat echo outputs a line of dashes repeat echo clears the screen Edit command Syntax edit file name This command invokes the ASCII text editor specified by the EDITOR environment variable By default all equation spaces are edited Access to shell bin sh is required for this command to work Type edit atthe Mathomatic prompt to edit all expressions and equations you have entered for the current session When you are done editing Mathomatic expressions and commands save and exit the editor to have them automatically read in by Mathomatic If Mathomatic gets an error reading in its new input observe where the error is and continue to automatically re enter the editor To edit an existing file and have it read in specify the file name on the edit command line Eliminate command Syntax eliminate variables or all using equation number Echo command 25 Mathomatic Command Reference 10 23 2012 This command is used to combine simultaneous equations by automatically substituting variables in the current equation It will scan the command line from left to right replacing all occurrences of t
76. sed If the startup file doesn t exist or something is wrong then an error message is displayed and this set command returns with failure Options set precision followed by an integer less than or equal to 15 sets the display precision in number of decimal digits for most numerical output All arithmetic in Mathomatic is double precision floating point so it is not useful to set this higher than 15 digits Display output is rounded to the precision set by this option though internally all constants are rounded to fit in a double precision float data type of about 15 decimal digits precision The default for this display precision set variable is 14 digits set no autosolve will turn off solving by typing the solve variable at the main prompt unless an equals sign is included This allows entry of single variable expressions into equation spaces Solving is always allowed using the solve command set no autocalc will turn off automatic approximation and display with the calculate command of purely numerical input entered at the main prompt Numerical expressions are simply entered as is when this option is turned off When autocalc is on the current calculation is deleted when the next calculation is entered if set autodelete is specified otherwise it remains in memory for later use The default is no autodelete so to be helpful all old numeric calculations are automatically deleted from memory if memory ever becomes exhausted
77. selected equation spaces by multiplying out products of sums and exponentiated sums and then simplifying a little displaying the results One or more options may be specified like count which also displays the number of additive terms To illustrate what unfactoring does more often known as expanding suppose you have the following equations 1 gt a b ctd 1 a b c d 1 gt z xty 2 Taylor command 50 Mathomatic Command Reference 10 23 2012 2 2 x y 2 2 gt unfactor all 1 a b c b d 2 Z x 2 2 x y y 2 2 gt x y 2 is called an exponentiated sum and is converted to x y x y and then multiplied out unless the quick option is given Because this is a general but inefficient expansion method exponentiated sums usually fail expansion when the power is greater than 10 growing larger than will fit in an equation space It is also CPU time consuming so unfactor quick and simplify quick were created to only expand products of sums and not exponentiated sums The opposite of unfactoring is factoring Careful and neat factoring is always done by the simplify command unfactor fraction by itself expands algebraic fractions by also expanding division of sums multiplying out each fraction with a sum in the numerator into the sum of smaller fractions with the same denominator for each term in numerator See the example under the fraction command unfactor power do
78. splayed This command can be shortened to set factor set right_associative_power associates power operators from right to left in the absence of parentheses so that x a b is interpreted as x a b Other math programs typically associate power operators from right to left The default is set no right which associates power operators the same as all other operators in Mathomatic from left to right resulting in xa b set plot_prefix followed by a string of 8 bit characters will prepend the string to the gnuplot plot string when using the Mathomatic plot command For example set plot set polar typed at the Mathomatic main prompt will allow 2D polar plots with subsequent plot commands using variable t instead of x set special_variable_characters followed by a string of 8 bit characters will allow Mathomatic to use those characters in variable names in addition to the normal variable name characters which are the alphanumeric characters and underline _ For example set special will allow variable names like a and a and set special will allow entry of array elements like a 3 for simulated array arithmetic Most non alphanumeric characters in variable names are converted to underline characters _ when exporting to a programming language or to a different program set directory followed by a directory name will change the current working directory to that directory Not specifying a directory name def
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80. t to the present version but may differ in detail to address new problems or concerns See http www gnu org copyleft 7 AGGREGATION WITH INDEPENDENT WORBS GNU Free Documentation License 10 23 2012 Each version of the License is given a distinguishing version number If the Document specifies that a particular numbered version of this License or any later version applies to it you have the option of following the terms and conditions either of that specified version or of any later version that has been published not as a draft by the Free Software Foundation If the Document does not specify a version number of this License you may choose any version ever published not as a draft by the Free Software Foundation If the Document specifies that a proxy can decide which future versions of this License can be used that proxy s public statement of acceptance of a version permanently authorizes you to choose that version for the Document 11 RELICENSING Massive Multiauthor Collaboration Site or MMC Site means any World Wide Web server that publishes copyrightable works and also provides prominent facilities for anybody to edit those works A public wiki that anybody can edit is an example of such a server A Massive Multiauthor Collaboration or MMC contained in the site means any set of copyrightable works thus published on the MMC site CC BY SA means the Creative Commons Attribution Share Alike 3 0 license published by
81. the documentation index www mathomatic org Commands 11 Mathomatic Command Reference 10 23 2012 Mathomatic Command Reference Topics 1 Introduction 2 Entering Commands 3 Selecting Expressions 4 Solving Equations 5 Documentation License Commands Approximate Divide Help Pause Replace Taylor Calculate Echo Imaginary Plot Roots Unfactor Clear Edit Integrate Product Save Variables Code Eliminate Laplace Push Set Version Compare Extrema Limit Quit Simplify Copy Factor List Read Solve Derivative For Nintegrate Real Sum Display Fraction Optimize Repeat Tally Mathomatic User Guide Introduction LHS is shorthand for the Left Hand Side of an equation Similarly RHS used here always means the Right Hand Side In this document text enclosed by straight brackets like this means it is optional and may be omitted The word expression without double quotes always means a mathematical expression or formula At the Mathomatic main prompt you may enter e A numerical expression which is stored then instantly approximated evaluated and displayed with the calculate command this is the autocalc option To skip running the calculate command on the numerical input just set it equal to any normal variable e A new algebraic expression or equation which is stored and made the current equation e A new expression followed by an equals sign to set the current non equation equal to making it an equation or to sto
82. the logarithm function has not yet been implemented in the Mathomatic symbolic math engine If you are wondering what to try first in Mathomatic type help examples at the Mathomatic prompt Color mode is toggled by the c option on the shell command line like this mathomatic c ANSI color mode is the default which outputs ANSI terminal escape sequences to make each level of parentheses a different color improving readability If ANSI color mode is on an ANSI compatible terminal emulator is required If the colors are hard to see use the b option instead which will always turn on bold color mode increasing the color brightness The other options are described in the Unix Linux man page for Mathomatic After any options text files may be specified on the shell command line that will be automatically read in with the read command unless the e option is specified in which case mathematical expressions and Mathomatic commands are expected separated by unquoted space characters It is recommended that the name mathomatic be shortened to am and e for quicker and easier access from the shell command line This can be done in the Bash shell by adding the following two lines to your bashrc file Developer Information 3 Mathomatic User Guide 10 23 2012 alias am mathomatic alias e mathomatic e Then just typing am at the shell prompt will run Mathomatic as an interactive application Typing e followed by a quoted ma
83. the terms of this License in the form shown in the Addendum below e G Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document s license notice e H Include an unaltered copy of this License e I Preserve the section Entitled History Preserve its Title and add to it an item stating at least the title year new authors and publisher of the Modified Version as given on the Title Page If there is no section Entitled History in the Document create one stating the title year authors and publisher of the Document as given on its Title Page then add an item describing the Modified Version as stated in the previous sentence e J Preserve the network location if any given in the Document for public access to a Transparent copy of the Document and likewise the network locations given in the Document for previous versions it was based on These may be placed in the History section You may omit a network location for a work that was published at least four years before the Document itself or if the original publisher of the version it refers to gives permission e K For any section Entitled Acknowledgements or Dedications Preserve the Title of the section and preserve in the section all the substance and tone of each of the contributor acknowledgements and or dedications given therein e L Preserve all the Invariant Sections of the Document unaltered in their text and in
84. their titles Section numbers or the equivalent are not considered part of the section titles e M Delete any section Entitled Endorsements Such a section may not be included in the Modified Version e N Do not retitle any existing section to be Entitled Endorsements or to conflict in title with any Invariant Section e O Preserve any Warranty Disclaimers If the Modified Version includes new front matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document you may at your option designate some or all of these sections as invariant To do this add their titles to the list of Invariant Sections in the Modified Version s license notice These titles must be distinct from any other section titles You may add a section Entitled Endorsements provided it contains nothing but endorsements of your Modified Version by various parties for example statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard 4 MODIFICATIONS 56 GNU Free Documentation License 10 23 2012 You may add a passage of up to five words as a Front Cover Text and a passage of up to 25 words as a Back Cover Text to the end of the list of Cover Texts in the Modified Version Only one passage of Front Cover Text and one of Back Cover Text may be added by or through arrangements made by any one entity If the Document already includes a cover tex
85. thematical expression at the shell prompt will quickly and silently bring up Mathomatic and calculate and display the result am stands for algebraic manipulator and e stands for evaluate Equations and Expressions On the World Wide Web are some simple algebra texts like those at MathsIsFun com for some basic algebra definitions suitable for children and of course The Simple English Wikipedia which is usually easier to understand than The English Wikipedia The English Wikipedia contains much more advanced mathematics Mathematical equations and expressions are entered into Mathomatic equation spaces by typing pasting or reading them in at the main prompt The maximum number and size of available equation spaces is displayed every time Mathomatic starts up When an expression grows larger than half the equation space size processing stops and the Expression too large message is displayed returning you to the main prompt The reason it does this is because each equation space consists of two equation sides which are fixed size arrays that are easily manipulated by the software Each equation space is successively numbered with an equation number starting at 1 The main prompt 1 gt contains the equation number of the current equation space The current equation can be changed by typing a valid equation number at the main prompt called selecting an equation space or by entering another equation or expression which be
86. tive to the current equation instead of an absolute equation number This syntax also works when prompted for an expression the RHS or the expression at that equation number is substituted every place equation number is entered Autoselect feature Selecting an equation space to make it the current equation is now conveniently done by typing only the equation number at the main prompt This is called the set autoselect option Solving Equations Syntax variable or 0 Mathomatic can solve symbolic equations for any variable or for zero Solving is accomplished internally by applying identical mathematical operations to both sides of the equation and simplifying or by plugging the general coefficients of the solve variable into the quadratic formula The Mathomatic solve algorithm is the best possible for general algebra however the result is not checked by plugging the solutions into the original equation unless the solve verify command is used for solving To require confirmed correctness of the solutions in this way use the solve verifiable command To automatically solve the current equation for a variable type the variable name at the main prompt Mathomatic will proceed to manipulate the current equation until all of the solutions for the specified Entering Commands 14 Mathomatic Command Reference 10 23 2012 variable are determined If successful the current equation is replaced with the solutions and then displayed
87. wise the current equation remains unchanged after this copy command Derivative command Syntax derivative nosimplify variable or all order Compare command 21 Mathomatic Command Reference 10 23 2012 Alternate command name differentiate This command computes the exact symbolic derivative of a function with respect to the specified variable using the current expression or RHS of the current equation as the function It does this by recursively applying the proper rule of differentiation for each operator encountered The result is quick simplified with the simplify quick command unless the nosimplify option is specified If successful the derivative is placed in the next available equation space displayed and becomes the current equation The original equation is not modified Specifying all computes the derivative of the current expression with respect to all normal variables It is equivalent to adding together the derivatives with respect to each normal variable Specifying the order allows you to repeatedly differentiate and simplify The default is to differentiate once order 1 If differentiation fails it is probably because symbolic logarithms are required Symbolic logarithms are not implemented in Mathomatic yet Also the factorial modulus and integral divide operators cannot be differentiated if they contain the specified variable Because this command handles almost everything a numerical different
88. without asking Note that any debugging output will be redirected too Two greater than characters gt gt next to each other will append command output to a file like the Unix shell does For example the Mathomatic command Introduction 13 Mathomatic Command Reference 10 23 2012 list export all gt filename will output all stored expressions and equations to a file in exportable single line per equation format so they can be read in by a different math program list is the command export is the option word and all is the equation number range Command option words such as export in the above list command line always come immediately after the command name and before anything else on the command line These words direct the command to do a different but related task If Mathomatic becomes unresponsive a rare occurrence pressing Control C once will usually safely abort the current operation and return you to the main prompt If not pressing Control C three times in a row will exit Mathomatic with a warning displayed the second time Selecting Expressions Syntax or Jequation number new expression To change the current equation at the main prompt and display it or replace it type a pound sign followed by the equation space number you wish to select possibly followed by a new expression to replace it with The equation number may be preceded by plus or minus to select an equation rela
89. yed otherwise Solution might be incorrect is displayed Expressions that are not equations Non equations that is any mathematical expression without an equals sign may be entered into equation spaces too However if the expression entered at the main prompt contains no variables it will be calculated and displayed with the calculate command unless the autocalc or auto option is turned off Non equations cannot be solved unless you set them equal to zero or something then they become an equation Non equations are stored in the first equation side LHS for that equation space The RHS will be empty size 0 Constants In Mathomatic numeric arithmetic is double precision floating point with about 14 decimal digits accuracy Many results will be exact because symbolic math is an exact math and because multiple floating point numbers can be combined for a single mathematical value for example 2 1 3 which is the cube root of 2 exactly Constants are approximated real numbers stored internally as IEEE 754 standard 64 bit 8 bytes double precision floating point values They may be entered as decimal base 10 numbers in normal notation or in scientific notation also called exponential notation Constants may also be entered in hexadecimal base 16 by starting them with Ox Constants are displayed in decimal base 10 rounded to 14 digits using either normal or scientific notation whichever is shortest Results are usually a

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