number of solutions of a regular chain - Maple Help

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RegularChains[ChainTools][NumberOfSolutions] - number of solutions of a regular chain

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

withRegularChains:

withChainTools:

R:=PolynomialRingx,a,b,c

R:=polynomial_ring

(1)

sys:=ax2+bx+c

sys:=ax2+bx+c

(2)

dec:=Triangularizesys,R,output=lazard

dec:=regular_chain,regular_chain

(3)

mapEquations,dec,R

ax2+bx+c,bx+c,a

(4)

mapDimension,dec,R

1,0

(5)

mapNumberOfSolutions,dec,R

∞,1

(6)

See Also

Dimension, Equations, PolynomialRing, RegularChains, SeparateSolutions, Triangularize


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