Quotient and remainder
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Syntax
[Q,R] =quorem(A,B,var)
[Q,R] =quorem(A,B)
Description
[Q,R] =quorem(A,B,var) divides A by B and returns the quotient Q and remainder R of the division, such that A = Q*B + R. This syntax regards A and B as polynomials in the variable var.
If A and B are matrices, quorem performs elements-wise division, using var as a variable. It returns the quotient Q and remainder R of the division, such that A = Q.*B + R.
[Q,R] =quorem(A,B) uses the variable determined by symvar(A,1). If symvar(A,1) returns an empty symbolic object sym([]), then quorem uses the variable determined by symvar(B,1).
If both symvar(A,1) and symvar(B,1) are empty, then A and B must both be integers or matrices with integer elements. In this case, quorem(A,B) returns symbolic integers Q and R, such that A = Q*B + R. If A and B are matrices, then Q and R are symbolic matrices with integer elements, such that A = Q.*B + R, and each element of R is smaller in absolute value than the corresponding element of B.
Examples
Divide Multivariate Polynomials
Compute the quotient and remainder of the division of these multivariate polynomials with respect to the variable y:
syms x yp1 = x^3*y^4 - 2*x*y + 5*x + 1;p2 = x*y;[q, r] = quorem(p1, p2, y)
q =x^2*y^3 - 2 r =5*x + 1
Divide Univariate Polynomials
Compute the quotient and remainder of the division of these univariate polynomials:
syms xp = x^3 - 2*x + 5;[q, r] = quorem(x^5, p)
q =x^2 + 2r =- 5*x^2 + 4*x - 10
Divide Integers
Compute the quotient and remainder of the division of these integers:
[q, r] = quorem(sym(10)^5, sym(985))
q =101 r =515
Input Arguments
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A — Dividend (numerator)
symbolic integer | polynomial | symbolic vector | symbolic matrix
Dividend (numerator), specified as a symbolic integer, polynomial, or a vector or matrix of symbolic integers or polynomials.
B — Divisor (denominator)
symbolic integer | polynomial | symbolic vector | symbolic matrix
Divisor (denominator), specified as a symbolic integer, polynomial, or a vector or matrix of symbolic integers or polynomials.
var — Polynomial variable
symbolic variable
Polynomial variable, specified as a symbolic variable.
Output Arguments
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Q — Quotient of the division
symbolic integer | symbolic expression | symbolic vector | symbolic matrix
Quotient of the division, returned as a symbolic integer, expression, or a vector or matrix of symbolic integers or expressions.
R — Remainder of the division
symbolic integer | symbolic expression | symbolic vector | symbolic matrix
Remainder of the division, returned as a symbolic integer, expression, or a vector or matrix of symbolic integers or expressions.
Version History
Introduced before R2006a
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