inert rem function - Maple Help

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Rem - inert rem function

Quo - inert quo function

Calling Sequence

Rem(a, b, x)

Rem(a, b, x, 'q')

Quo(a, b, x)

Quo(a, b, x, 'r')

Parameters

x

-

name (variable)

a, b

-

polynomials in x

q, r

-

unevaluated name

Description

• 

The Rem and Quo functions are placeholders for representing the remainder and quotient respectively of a divided by b where a and b are polynomials in the variable x over a field.  They are used in conjunction with either  mod  or  evala  as described below which define the coefficient domain.

• 

Functionality:  Rem returns the remainder r and if the fourth argument q is present then the quotient is assigned to q. Quo returns the quotient q and if the fourth argument r is present then the remainder is assigned to r. The remainder r and quotient q satisfy:  a=bq+r.

• 

The calls Rema,b,xmodp and Quoa,b,xmodp  compute the remainder and quotient respectively of a divided by b modulo p, a prime integer. The coefficients of a and b must be rational expressions over the rationals or over a finite field specified by RootOf expressions.  In particular, if the coefficients are integers then the computation is done over the field of integers modulo p.

• 

The calls evalaRema,b,x  and evalaQuoa,b,x compute the remainder and quotient respectively of a and b, where the coefficients of a and b are multivariate polynomials with coefficients in an algebraic number (or function) field.

Examples

a:=x4+5x3+6:

b:=x2+2x+7:

r:=Rema,b,x,'q'mod13

r:=5x+6

(1)

q

x2+3x

(2)

Expandabqrmod13

0

(3)

c:=x2x+3:

d:=xRootOf_Z23:

evalaQuoc,d,x

RootOf_Z231+x

(4)

evalaRemc,d,x

6RootOf_Z23

(5)

See Also

Divide, evala, mod, Powmod, quo, rem, RootOf


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