# Singular

##### 7.7.7.0. lpMaxIdeal
Procedure from library `fpadim.lib` (see fpadim_lib).

Usage:
lpMaxIdeal(d, donly); d an integer, donly an integer
RETURN: ideal
PURPOSE: computes a list of free monomials of degree at most d
if donly <> 0, only monomials of degree d are returned ASSUME: - basering is a Letterplace ring.
- d <= attrib(basering,uptodeg) holds. NOTE: analogous to maxideal(d) in the commutative case

Example:
 ```LIB "fpadim.lib"; ring r = 0,(a,b,c),dp; def R = makeLetterplaceRing(7); setring R; lpMaxIdeal(1,0); ==> _[1]=c(1) ==> _[2]=b(1) ==> _[3]=a(1) lpMaxIdeal(2,0); ==> _[1]=c(1) ==> _[2]=b(1) ==> _[3]=a(1) ==> _[4]=a(1)*c(2) ==> _[5]=a(1)*b(2) ==> _[6]=a(1)*a(2) ==> _[7]=b(1)*c(2) ==> _[8]=b(1)*b(2) ==> _[9]=b(1)*a(2) ==> _[10]=c(1)*c(2) ==> _[11]=c(1)*b(2) ==> _[12]=c(1)*a(2) lpMaxIdeal(2,1); ==> _[1]=a(1)*c(2) ==> _[2]=a(1)*b(2) ==> _[3]=a(1)*a(2) ==> _[4]=b(1)*c(2) ==> _[5]=b(1)*b(2) ==> _[6]=b(1)*a(2) ==> _[7]=c(1)*c(2) ==> _[8]=c(1)*b(2) ==> _[9]=c(1)*a(2) lpMaxIdeal(4,0); ==> _[1]=c(1) ==> _[2]=b(1) ==> _[3]=a(1) ==> _[4]=a(1)*c(2) ==> _[5]=a(1)*b(2) ==> _[6]=a(1)*a(2) ==> _[7]=b(1)*c(2) ==> _[8]=b(1)*b(2) ==> _[9]=b(1)*a(2) ==> _[10]=c(1)*c(2) ==> _[11]=c(1)*b(2) ==> _[12]=c(1)*a(2) ==> _[13]=c(1)*a(2)*c(3) ==> _[14]=c(1)*a(2)*b(3) ==> _[15]=c(1)*a(2)*a(3) ==> _[16]=c(1)*b(2)*c(3) ==> _[17]=c(1)*b(2)*b(3) ==> _[18]=c(1)*b(2)*a(3) ==> _[19]=c(1)*c(2)*c(3) ==> _[20]=c(1)*c(2)*b(3) ==> _[21]=c(1)*c(2)*a(3) ==> _[22]=b(1)*a(2)*c(3) ==> _[23]=b(1)*a(2)*b(3) ==> _[24]=b(1)*a(2)*a(3) ==> _[25]=b(1)*b(2)*c(3) ==> _[26]=b(1)*b(2)*b(3) ==> _[27]=b(1)*b(2)*a(3) ==> _[28]=b(1)*c(2)*c(3) ==> _[29]=b(1)*c(2)*b(3) ==> _[30]=b(1)*c(2)*a(3) ==> _[31]=a(1)*a(2)*c(3) ==> _[32]=a(1)*a(2)*b(3) ==> _[33]=a(1)*a(2)*a(3) ==> _[34]=a(1)*b(2)*c(3) ==> _[35]=a(1)*b(2)*b(3) ==> _[36]=a(1)*b(2)*a(3) ==> _[37]=a(1)*c(2)*c(3) ==> _[38]=a(1)*c(2)*b(3) ==> _[39]=a(1)*c(2)*a(3) ==> _[40]=a(1)*c(2)*a(3)*c(4) ==> _[41]=a(1)*c(2)*a(3)*b(4) ==> _[42]=a(1)*c(2)*a(3)*a(4) ==> _[43]=a(1)*c(2)*b(3)*c(4) ==> _[44]=a(1)*c(2)*b(3)*b(4) ==> _[45]=a(1)*c(2)*b(3)*a(4) ==> _[46]=a(1)*c(2)*c(3)*c(4) ==> _[47]=a(1)*c(2)*c(3)*b(4) ==> _[48]=a(1)*c(2)*c(3)*a(4) ==> _[49]=a(1)*b(2)*a(3)*c(4) ==> _[50]=a(1)*b(2)*a(3)*b(4) ==> _[51]=a(1)*b(2)*a(3)*a(4) ==> _[52]=a(1)*b(2)*b(3)*c(4) ==> _[53]=a(1)*b(2)*b(3)*b(4) ==> _[54]=a(1)*b(2)*b(3)*a(4) ==> _[55]=a(1)*b(2)*c(3)*c(4) ==> _[56]=a(1)*b(2)*c(3)*b(4) ==> _[57]=a(1)*b(2)*c(3)*a(4) ==> _[58]=a(1)*a(2)*a(3)*c(4) ==> _[59]=a(1)*a(2)*a(3)*b(4) ==> _[60]=a(1)*a(2)*a(3)*a(4) ==> _[61]=a(1)*a(2)*b(3)*c(4) ==> _[62]=a(1)*a(2)*b(3)*b(4) ==> _[63]=a(1)*a(2)*b(3)*a(4) ==> _[64]=a(1)*a(2)*c(3)*c(4) ==> _[65]=a(1)*a(2)*c(3)*b(4) ==> _[66]=a(1)*a(2)*c(3)*a(4) ==> _[67]=b(1)*c(2)*a(3)*c(4) ==> _[68]=b(1)*c(2)*a(3)*b(4) ==> _[69]=b(1)*c(2)*a(3)*a(4) ==> _[70]=b(1)*c(2)*b(3)*c(4) ==> _[71]=b(1)*c(2)*b(3)*b(4) ==> _[72]=b(1)*c(2)*b(3)*a(4) ==> _[73]=b(1)*c(2)*c(3)*c(4) ==> _[74]=b(1)*c(2)*c(3)*b(4) ==> _[75]=b(1)*c(2)*c(3)*a(4) ==> _[76]=b(1)*b(2)*a(3)*c(4) ==> _[77]=b(1)*b(2)*a(3)*b(4) ==> _[78]=b(1)*b(2)*a(3)*a(4) ==> _[79]=b(1)*b(2)*b(3)*c(4) ==> _[80]=b(1)*b(2)*b(3)*b(4) ==> _[81]=b(1)*b(2)*b(3)*a(4) ==> _[82]=b(1)*b(2)*c(3)*c(4) ==> _[83]=b(1)*b(2)*c(3)*b(4) ==> _[84]=b(1)*b(2)*c(3)*a(4) ==> _[85]=b(1)*a(2)*a(3)*c(4) ==> _[86]=b(1)*a(2)*a(3)*b(4) ==> _[87]=b(1)*a(2)*a(3)*a(4) ==> _[88]=b(1)*a(2)*b(3)*c(4) ==> _[89]=b(1)*a(2)*b(3)*b(4) ==> _[90]=b(1)*a(2)*b(3)*a(4) ==> _[91]=b(1)*a(2)*c(3)*c(4) ==> _[92]=b(1)*a(2)*c(3)*b(4) ==> _[93]=b(1)*a(2)*c(3)*a(4) ==> _[94]=c(1)*c(2)*a(3)*c(4) ==> _[95]=c(1)*c(2)*a(3)*b(4) ==> _[96]=c(1)*c(2)*a(3)*a(4) ==> _[97]=c(1)*c(2)*b(3)*c(4) ==> _[98]=c(1)*c(2)*b(3)*b(4) ==> _[99]=c(1)*c(2)*b(3)*a(4) ==> _[100]=c(1)*c(2)*c(3)*c(4) ==> _[101]=c(1)*c(2)*c(3)*b(4) ==> _[102]=c(1)*c(2)*c(3)*a(4) ==> _[103]=c(1)*b(2)*a(3)*c(4) ==> _[104]=c(1)*b(2)*a(3)*b(4) ==> _[105]=c(1)*b(2)*a(3)*a(4) ==> _[106]=c(1)*b(2)*b(3)*c(4) ==> _[107]=c(1)*b(2)*b(3)*b(4) ==> _[108]=c(1)*b(2)*b(3)*a(4) ==> _[109]=c(1)*b(2)*c(3)*c(4) ==> _[110]=c(1)*b(2)*c(3)*b(4) ==> _[111]=c(1)*b(2)*c(3)*a(4) ==> _[112]=c(1)*a(2)*a(3)*c(4) ==> _[113]=c(1)*a(2)*a(3)*b(4) ==> _[114]=c(1)*a(2)*a(3)*a(4) ==> _[115]=c(1)*a(2)*b(3)*c(4) ==> _[116]=c(1)*a(2)*b(3)*b(4) ==> _[117]=c(1)*a(2)*b(3)*a(4) ==> _[118]=c(1)*a(2)*c(3)*c(4) ==> _[119]=c(1)*a(2)*c(3)*b(4) ==> _[120]=c(1)*a(2)*c(3)*a(4) lpMaxIdeal(4,1); ==> _[1]=a(1)*c(2)*a(3)*c(4) ==> _[2]=a(1)*c(2)*a(3)*b(4) ==> _[3]=a(1)*c(2)*a(3)*a(4) ==> _[4]=a(1)*c(2)*b(3)*c(4) ==> _[5]=a(1)*c(2)*b(3)*b(4) ==> _[6]=a(1)*c(2)*b(3)*a(4) ==> _[7]=a(1)*c(2)*c(3)*c(4) ==> _[8]=a(1)*c(2)*c(3)*b(4) ==> _[9]=a(1)*c(2)*c(3)*a(4) ==> _[10]=a(1)*b(2)*a(3)*c(4) ==> _[11]=a(1)*b(2)*a(3)*b(4) ==> _[12]=a(1)*b(2)*a(3)*a(4) ==> _[13]=a(1)*b(2)*b(3)*c(4) ==> _[14]=a(1)*b(2)*b(3)*b(4) ==> _[15]=a(1)*b(2)*b(3)*a(4) ==> _[16]=a(1)*b(2)*c(3)*c(4) ==> _[17]=a(1)*b(2)*c(3)*b(4) ==> _[18]=a(1)*b(2)*c(3)*a(4) ==> _[19]=a(1)*a(2)*a(3)*c(4) ==> _[20]=a(1)*a(2)*a(3)*b(4) ==> _[21]=a(1)*a(2)*a(3)*a(4) ==> _[22]=a(1)*a(2)*b(3)*c(4) ==> _[23]=a(1)*a(2)*b(3)*b(4) ==> _[24]=a(1)*a(2)*b(3)*a(4) ==> _[25]=a(1)*a(2)*c(3)*c(4) ==> _[26]=a(1)*a(2)*c(3)*b(4) ==> _[27]=a(1)*a(2)*c(3)*a(4) ==> _[28]=b(1)*c(2)*a(3)*c(4) ==> _[29]=b(1)*c(2)*a(3)*b(4) ==> _[30]=b(1)*c(2)*a(3)*a(4) ==> _[31]=b(1)*c(2)*b(3)*c(4) ==> _[32]=b(1)*c(2)*b(3)*b(4) ==> _[33]=b(1)*c(2)*b(3)*a(4) ==> _[34]=b(1)*c(2)*c(3)*c(4) ==> _[35]=b(1)*c(2)*c(3)*b(4) ==> _[36]=b(1)*c(2)*c(3)*a(4) ==> _[37]=b(1)*b(2)*a(3)*c(4) ==> _[38]=b(1)*b(2)*a(3)*b(4) ==> _[39]=b(1)*b(2)*a(3)*a(4) ==> _[40]=b(1)*b(2)*b(3)*c(4) ==> _[41]=b(1)*b(2)*b(3)*b(4) ==> _[42]=b(1)*b(2)*b(3)*a(4) ==> _[43]=b(1)*b(2)*c(3)*c(4) ==> _[44]=b(1)*b(2)*c(3)*b(4) ==> _[45]=b(1)*b(2)*c(3)*a(4) ==> _[46]=b(1)*a(2)*a(3)*c(4) ==> _[47]=b(1)*a(2)*a(3)*b(4) ==> _[48]=b(1)*a(2)*a(3)*a(4) ==> _[49]=b(1)*a(2)*b(3)*c(4) ==> _[50]=b(1)*a(2)*b(3)*b(4) ==> _[51]=b(1)*a(2)*b(3)*a(4) ==> _[52]=b(1)*a(2)*c(3)*c(4) ==> _[53]=b(1)*a(2)*c(3)*b(4) ==> _[54]=b(1)*a(2)*c(3)*a(4) ==> _[55]=c(1)*c(2)*a(3)*c(4) ==> _[56]=c(1)*c(2)*a(3)*b(4) ==> _[57]=c(1)*c(2)*a(3)*a(4) ==> _[58]=c(1)*c(2)*b(3)*c(4) ==> _[59]=c(1)*c(2)*b(3)*b(4) ==> _[60]=c(1)*c(2)*b(3)*a(4) ==> _[61]=c(1)*c(2)*c(3)*c(4) ==> _[62]=c(1)*c(2)*c(3)*b(4) ==> _[63]=c(1)*c(2)*c(3)*a(4) ==> _[64]=c(1)*b(2)*a(3)*c(4) ==> _[65]=c(1)*b(2)*a(3)*b(4) ==> _[66]=c(1)*b(2)*a(3)*a(4) ==> _[67]=c(1)*b(2)*b(3)*c(4) ==> _[68]=c(1)*b(2)*b(3)*b(4) ==> _[69]=c(1)*b(2)*b(3)*a(4) ==> _[70]=c(1)*b(2)*c(3)*c(4) ==> _[71]=c(1)*b(2)*c(3)*b(4) ==> _[72]=c(1)*b(2)*c(3)*a(4) ==> _[73]=c(1)*a(2)*a(3)*c(4) ==> _[74]=c(1)*a(2)*a(3)*b(4) ==> _[75]=c(1)*a(2)*a(3)*a(4) ==> _[76]=c(1)*a(2)*b(3)*c(4) ==> _[77]=c(1)*a(2)*b(3)*b(4) ==> _[78]=c(1)*a(2)*b(3)*a(4) ==> _[79]=c(1)*a(2)*c(3)*c(4) ==> _[80]=c(1)*a(2)*c(3)*b(4) ==> _[81]=c(1)*a(2)*c(3)*a(4) ```