# Difference between revisions of "ApCoCoA-1:DA.InitialOfDer"

From ApCoCoAWiki

S schuster (talk | contribs) |
S schuster (talk | contribs) |
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<command> | <command> | ||

− | <title> | + | <title>DA.InitialOfDer</title> |

− | <short_description>the initial wrt. a given derivative</short_description> | + | <short_description>Computes the initial wrt. a given derivative.</short_description> |

<syntax> | <syntax> | ||

− | + | DA.InitialOfDer(F:POLY, X:INDET):POLY | |

</syntax> | </syntax> | ||

<description> | <description> | ||

− | InitialOfDer returns the polynomial leading coefficient of polynomial F regarded as polynomial in the derivative X. | + | DA.InitialOfDer returns the polynomial leading coefficient of polynomial F regarded as polynomial in the derivative X. |

− | + | <itemize> | |

+ | <item>@param F A differential polynomial.</item> | ||

+ | <item>@param X A indeterminate.</item> | ||

+ | <item>@return Initial of F wrt. X.</item> | ||

+ | </itemize> | ||

<example> | <example> | ||

Use Q[x[1..2,0..20]]; | Use Q[x[1..2,0..20]]; | ||

− | Use Q[x[1..2,0..20]], Ord( | + | Use Q[x[1..2,0..20]], Ord(DA.DiffTO("Lex")); |

F:=x[1,2]^3x[2,2]^2 + x[1,1]^3x[2,2]^2 + 1/4x[1,2]; | F:=x[1,2]^3x[2,2]^2 + x[1,1]^3x[2,2]^2 + 1/4x[1,2]; | ||

− | + | DA.InitialOfDer(F, x[1,2]); | |

------------------------------- | ------------------------------- | ||

x[2,2]^2 | x[2,2]^2 | ||

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</example> | </example> | ||

</description> | </description> | ||

− | <see> | + | <types> |

− | <see> | + | <type>polynomial</type> |

+ | </types> | ||

+ | <see>DA.Initial</see> | ||

+ | <see>DA.DiffTO</see> | ||

+ | <key>InitialOfDer</key> | ||

+ | <key>DA.InitialOfDer</key> | ||

+ | <key>diffalg.InitialOfDer</key> | ||

+ | <key>differential.InitialOfDer</key> | ||

<wiki-category>Package_diffalg</wiki-category> | <wiki-category>Package_diffalg</wiki-category> | ||

</command> | </command> |

## Revision as of 13:32, 22 April 2009

## DA.InitialOfDer

Computes the initial wrt. a given derivative.

### Syntax

DA.InitialOfDer(F:POLY, X:INDET):POLY

### Description

DA.InitialOfDer returns the polynomial leading coefficient of polynomial F regarded as polynomial in the derivative X.

@param F A differential polynomial.

@param X A indeterminate.

@return Initial of F wrt. X.

#### Example

Use Q[x[1..2,0..20]]; Use Q[x[1..2,0..20]], Ord(DA.DiffTO("Lex")); F:=x[1,2]^3x[2,2]^2 + x[1,1]^3x[2,2]^2 + 1/4x[1,2]; DA.InitialOfDer(F, x[1,2]); ------------------------------- x[2,2]^2 -------------------------------