LongDivision - Maple Help

Student[Basics]

 LongDivision
 generate steps for numeric and polynomial long division

 Calling Sequence LongDivision( dividend, divisor ) LongDivision( dividend, divisor, variable )

Parameters

 dividend - integer, float, or polynomial divisor - integer, float, or polynomial variable - (optional) name appendresult - (optional) true or false digits - (optional) non-negative integer decimaldigits - (optional) non-negative integer output - (optional) one of typeset,string,qr,printf, canvas, or link; format of result

Description

 • The LongDivision command shows the steps in dividing dividend/divisor by constructing a tableau:

quotient

---------------

divisor ) dividend

... steps ...

 • This command shows the steps for integer, floating-point, and polynomial long division.
 • When divisor and/or dividend are polynomials, the inputs may first be rearranged in a standard form as returned by collect.  If no variable is given for which to collect the terms by, it picks a variable for you.
 • When appendresult=true, the output includes the result, quotient + remainder/divisor, in addition to the long division.  By default appendresult=false.
 • When dividing numbers, there are two similar options for controlling how far to proceed if a zero remainder is not reached.  Both options only apply after exhausting the digits in the dividend.  After this, the digits=n option causes division to continue until n significant digits have been computed in the quotient.  Alternately, the decimaldigits=m causes division to continue until m digits have been computed to the right of the decimal point in the quotient.
 • The default output format, typeset, is chosen for the best visual display in the standard document interface.  The output option can be set to printf for an alternate, character-based visual display. The string output is the same character-based format as printf, but returned as a string, so that it can be further processed in your own code.  Note that when the string output is displayed, it is center-formatted and will not look as good as output=printf.  The output=qr option returns a pair of values: the quotient as computed, and the number at the bottom of the tableau (the remainder for exact integer and polynomial division).
 • A MapleLearn canvas can be created that contains the long division output by using the option output=canvas or output=link.
 • The option output=link produces MathML representing the long division using the tag.
 • This function is part of the Student:-Basics package.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right):$
 > $\mathrm{LongDivision}\left(1001,30\right)$
 (1)
 > $\mathrm{LongDivision}\left(1001,30,'\mathrm{appendresult}'=\mathrm{true}\right)$
 (2)
 > $\mathrm{LongDivision}\left(1001,30,'\mathrm{decimaldigits}'=2\right)$
 (3)
 > $\mathrm{LongDivision}\left(48{x}^{4}+284{x}^{3}+620{x}^{2}+593x+210,2x+3\right)$
 $\begin{array}{cc}\stackrel{\phantom{{{z}}^{{2}}}}{{2}{}{x}{+}{3}}& \begin{array}{cccccc}{}& \phantom{{\mathrm{PPP}}}{24}{}{{x}}^{{3}}& \phantom{{\mathrm{PP}}}{+}{106}{}{{x}}^{{2}}& \phantom{{\mathrm{PP}}}{+}{151}{}{x}& \phantom{{\mathrm{PPP}}}{+}{70}& {}\\ {)}\phantom{{{x}}^{{2}}}& \phantom{{1}}{48}{}{{x}}^{{4}}& \phantom{{1}}{+}{284}{}{{x}}^{{3}}& \phantom{{1}}{+}{620}{}{{x}}^{{2}}& \phantom{{1}}{+}{593}{}{x}& \phantom{{1}}{+}{210}\\ {}& \multicolumn{2}{c}{\frac{{48}{}{{x}}^{{4}}{+}{72}{}{{x}}^{{3}}}{\phantom{{.}}}}& {}\\ {}& {}& \multicolumn{2}{c}{{212}{}{{x}}^{{3}}{+}{620}{}{{x}}^{{2}}}& {}& {}\\ {}& {}& \multicolumn{2}{c}{\frac{{212}{}{{x}}^{{3}}{+}{318}{}{{x}}^{{2}}}{\phantom{{.}}}}& {}& {}\\ {}& {}& {}& \multicolumn{2}{c}{{302}{}{{x}}^{{2}}{+}{593}{}{x}}& {}& {}& {}\\ {}& {}& {}& \multicolumn{2}{c}{\frac{{302}{}{{x}}^{{2}}{+}{453}{}{x}}{\phantom{{.}}}}& {}& {}& {}\\ {}& {}& {}& {}& \multicolumn{2}{c}{{140}{}{x}{+}{210}}& {}& {}& {}& {}\\ {}& {}& {}& {}& \multicolumn{2}{c}{\frac{{140}{}{x}{+}{210}}{\phantom{{.}}}}& {}& {}& {}& {}\\ {}& {}& {}& {}& {}& {0}\hfill & {}& {}& {}& {}& {}\end{array}\end{array}$ (4)
 > $\mathrm{LongDivision}\left(48{x}^{4}+284{x}^{3}+620{x}^{2}+593x+210,2x+3,'\mathrm{output}'='\mathrm{qr}'\right)$
 $\left[{24}{}{{x}}^{{3}}{+}{106}{}{{x}}^{{2}}{+}{151}{}{x}{+}{70}{,}{0}\right]$ (5)

Compatibility

 • The Student:-Basics:-LongDivision command was introduced in Maple 2021.