Add LTermNP, LTermsNP and LMonNP; also add FactorOutGcdNP

doc/examples/functions.g

@@ -471,6 +471,26 @@ PrintNPList(List(LMonsNP(Lnp), q -> [[q],[1]]));
 
 # <#/GAPDoc>
 
+# <#GAPDoc Label="example-LTermNP">
+# <E>Example:</E>
+# We put two polynomials in NP format into the list <C>Lnp</C>.
+# <L>
+p1 := [[[1,1,2],[1]],[6,-7]];;
+p2 := [[[1,2,2],[2]],[8,-9]];;
+Lnp := [p1,p2];;
+# </L>
+
+# The leading term of a polynomial is returned by <C>LTermNP</C>, 
+# and the list of leading terms is computed by <C>LTermsNP</C>:
+
+# <L>
+LTermNP(p1);
+LTnp := LTermsNP( Lnp );
+PrintNPList( LTnp ); 
+# </L>
+
+# <#/GAPDoc>
+
 # <#GAPDoc Label="example-MkMonicNP">
 # <E>Example:</E>
 # Consider the following polynomial in NP format.
@@ -479,13 +499,30 @@ p := [[[1,1,2],[]],[2,-1]];;
 PrintNP(p);
 # </L>
 
-# The coefficient of the leading term is <M>2</M>. The function <C>MkMonicNP</C> finds
-# this coefficient and divides all terms by it:
-
+# The coefficient of the leading term is <M>2</M>. 
+# The function <C>MkMonicNP</C> finds this coefficient 
+# and divides every term by it:
 # <L>
 PrintNP(MkMonicNP(p));
 # </L>
+# <#/GAPDoc>
 
+# <#GAPDoc Label="example-FactorOutGcdNP">
+# <E>Example:</E>
+# Consider the following polynomial in NP format.
+# <L>
+p := [[[1,1,2],[1,2],[1]],[30,70,105]];;
+PrintNP(p);
+# </L>
+
+# The <C>Gcd</C> of the coefficients <M>[30,70,105]</M> is <M>5</M>.
+# The function <C>FactorOutGcdNP</C> divides the polynomial by <M>5</M>:
+
+# <L>
+PrintNP(FactorOutGcdNP(p));
+m := MkMonicNP(p);
+#</L>
+fm := FactorOutGcdNP(m);
 # <#/GAPDoc>
 
 

doc/examples/functions.xml

@@ -520,6 +520,30 @@ gap> PrintNPList(List(LMonsNP(Lnp), q -> [[q],[1]]));
 
 <#/GAPDoc>
 
+<#GAPDoc Label="example-LTermNP">
+<E>Example:</E>
+We put two polynomials in NP format into the list <C>Lnp</C>.
+<Listing><![CDATA[
+gap> p1 := [[[1,1,2],[1]],[6,-7]];;
+gap> p2 := [[[1,2,2],[2]],[8,-9]];;
+gap> Lnp := [p1,p2];;
+]]></Listing>
+
+The leading term of a polynomial is returned by <C>LTermNP</C>, 
+and the list of leading terms is computed by <C>LTermsNP</C>:
+
+<Listing><![CDATA[
+gap> LTermNP(p1);
+[ [ 1, 1, 2 ], [ 6 ] ]
+gap> LTnp := LTermsNP( Lnp );
+[ [ [ [ 1, 1, 2 ] ], [ 6 ] ], [ [ [ 1, 2, 2 ] ], [ 8 ] ] ]
+gap> PrintNPList( LTnp );
+6a^2b
+8ab^2
+]]></Listing>
+
+<#/GAPDoc>
+
 <#GAPDoc Label="example-MkMonicNP">
 <E>Example:</E>
 Consider the following polynomial in NP format.
@@ -529,8 +553,9 @@ gap> PrintNP(p);
  2a^2b - 1 
 ]]></Listing>
 
-The coefficient of the leading term is <M>2</M>. The function <C>MkMonicNP</C> finds
-this coefficient and divides all terms by it:
+The coefficient of the leading term is <M>2</M>. 
+The function <C>MkMonicNP</C> finds this coefficient 
+and divides every term by it:
 
 <Listing><![CDATA[
 gap> PrintNP(MkMonicNP(p));
@@ -539,6 +564,29 @@ gap> PrintNP(MkMonicNP(p));
 
 <#/GAPDoc>
 
+<#GAPDoc Label="example-FactorOutGcdNP">
+<E>Example:</E>
+Consider the following polynomial in NP format.
+<Listing><![CDATA[
+gap> p := [[[1,1,2],[1,2],[1]],[30,70,105]];;
+gap> PrintNP(p);
+ 30a^2b + 70ab + 105a 
+]]></Listing>
+
+The <C>Gcd</C> of the coefficients <M>[30,70,105]</M> is <M>5</M>.
+The function <C>FactorOutGcdNP</C> divides the polynomial by <M>5</M>:
+
+<Listing><![CDATA[
+gap> PrintNP(FactorOutGcdNP(p));
+ 6a^2b + 14ab + 21a 
+gap> m := MkMonicNP(p);
+[ [ [ 1, 1, 2 ], [ 1, 2 ], [ 1 ] ], [ 1, 7/3, 7/2 ] ]
+gap> fm := FactorOutGcdNP(m); 
+fail
+]]></Listing>
+
+<#/GAPDoc>
+
 
 <#GAPDoc Label="example-MulNP">
 <E>Example:</E>

doc/gbnp_doc.xml

@@ -536,7 +536,9 @@ algebra with the same growth).
 		<#Include Label="GtNP">
 		<#Include Label="LtNP">
 		<#Include Label="LMonsNP"> <!-- here ?? -->
+		<#Include Label="LTermsNP"> 
 		<#Include Label="MkMonicNP">
+		<#Include Label="FactorOutGcdNP">
 		<#Include Label="MulNP">
 	</Section>
 	<Section Label="grobner"><Heading>Gröbner functions, standard variant</Heading>

lib/nparith.gd

@@ -25,9 +25,13 @@
 
 DeclareGlobalFunction("LtNP");
 DeclareGlobalFunction("GtNP");
+DeclareGlobalFunction("LMonNP");
 DeclareGlobalFunction("LMonsNP");
+DeclareGlobalFunction("LTermNP");
+DeclareGlobalFunction("LTermsNP");
 DeclareGlobalFunction("CleanNP");
 DeclareGlobalFunction("MkMonicNP");
+DeclareGlobalFunction("FactorOutGcdNP");
 DeclareGlobalFunction("AddNP");
 DeclareGlobalFunction("MulNP");
 DeclareGlobalFunction("BimulNP");