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DifferentialAlgebra[Tools]

  

DeltaPolynomial

  

returns a Delta-polynomial

 

Calling Sequence

Parameters

Options

Description

Examples

Calling Sequence

DeltaPolynomial (p, q, R,opts)

Parameters

p

-

a differential polynomial

q

-

a differential polynomial

R

-

a differential polynomial ring or ideal

opts (optional)

-

a sequence of options

Options

• 

The opts arguments may contain one or more of the options below.

• 

notation = jet, tjet, diff or Diff. Specifies the notation used for the result of the function call. If not specified, the notation of R or of ideal is used.

• 

memout = nonnegative. Specifies a memory limit, in MB, for the computation. Default is zero (no memory out).

Description

• 

The function call DeltaPolynomial (p, q, R) returns the Δ-polynomial generated by p and q, which are regarded as differential polynomials of R, or, of its embedding ring, if R is an ideal. See DifferentialAlgebra for the definition of Δ-polynomials.

• 

The numeric coefficients of the returned Δ-polynomial are normalized: their gcd is equal to 1, and, the leading one is positive. It is required that the leading derivatives of p and q are derivatives of some same dependent variable.

• 

This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form DeltaPolynomial(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][DeltaPolynomial](...).

Examples

withDifferentialAlgebra:withTools:

RDifferentialRingderivations=x,y,blocks=u,v

R:=differential_ring

(1)

The triangular case: the least common derivative of the two leading derivatives is different from both of them.

DeltaPolynomialuxv,uy,R

vy

(2)

The non-triangular case: the leading derivative of the second argument is a derivative of the leading derivative of the first one.

DeltaPolynomialux24u,ux,x,R

ux

(3)

See Also

DifferentialAlgebra

LeadingDerivative

 


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