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RegularChains[ChainTools]

  

NumberOfSolutions

  

number of solutions of a regular chain

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

NumberOfSolutions(rc, R)

Parameters

rc

-

regular chain of R

R

-

polynomial ring

Description

• 

The command NumberOfSolutions(rc, R) returns the number of complex solutions of rc.

• 

If rc has a positive dimension, then infinity is returned.

• 

If rc has dimension zero, the number of roots is returned.

• 

This command is part of the RegularChains[ChainTools] package, so it can be used in the form NumberOfSolutions(..) only after executing the command with(RegularChains[ChainTools]). However, it can always be accessed through the long form of the command by using RegularChains[ChainTools][NumberOfSolutions](..).

Examples

with(RegularChains):

with(ChainTools):

R := PolynomialRing([x, a], {b, c});

Rpolynomial_ring

(1)

sys := [a*x^2+b*x+c];

sysax2+bx+c

(2)

dec := Triangularize(sys, R, output=lazard);

decregular_chain,regular_chain

(3)

map(Equations, dec, R);

ax2+bx+c,bx+c,a

(4)

map(Dimension, dec, R);

1,0

(5)

map(NumberOfSolutions, dec, R);

,1

(6)

See Also

Dimension

Equations

PolynomialRing

RegularChains

SeparateSolutions

Triangularize