def mono_total_next_grevlex ( m, n, x ):
#*****************************************************************************80
#
## MONO_TOTAL_NEXT_GREVLEX: grevlex next monomial, total degree equal to N.
#
# Discussion:
#
# We consider all monomials in an M-dimensional space, with total
# degree N.
#
# For example:
#
# M = 3
# N = 3
#
# # X(1) X(2) X(3) Degree
# +------------------------
# 1 | 0 0 3 3
# 2 | 0 1 2 3
# 3 | 1 0 2 3
# 4 | 0 2 1 3
# 5 | 1 1 1 3
# 6 | 2 0 1 3
# 7 | 0 3 0 3
# 8 | 1 2 0 3
# 9 | 2 1 0 3
# 10 | 3 0 0 3
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 24 October 2014
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer M, the spatial dimension.
#
# Input, integer N, the total degree.
# 0 <= N1 <= N2.
#
# Input, integer X[M], the current monomial.
# The first element is X = [ 0, 0, ..., 0, N ].
# The last is [ N, 0, ..., 0, 0 ].
#
# Output, integer X[M], the next monomial.
#
from i4vec_sum import i4vec_sum
from mono_next_grevlex import mono_next_grevlex
if ( n < 0 ):
print ''
print 'MONO_TOTAL_NEXT_GREVLEX - Fatal error!'
print ' N < 0.'
sys.exit ( 'MONO_TOTAL_NEXT_GREVLEX - Fatal error!' )
if ( i4vec_sum ( m, x ) != n ):
print ''
print 'MONO_TOTAL_NEXT_GREVLEX - Fatal error!'
print ' Input X sums is not N.'
sys.exit ( 'MONO_TOTAL_NEXT_GREVLEX - Fatal error!' )
if ( n == 0 ):
return x
if ( x[0] == n ):
x[0] = 0
x[m-1] = n
else:
x = mono_next_grevlex ( m, x )
return x
def mono_upto_next_grevlex ( m, n, x ):
#*****************************************************************************80
#
## MONO_UPTO_NEXT_GREVLEX: grevlex next monomial, total degree up to N.
#
# Discussion:
#
# We consider all monomials in an M-dimensional space, with total
# degree N.
#
# For example:
#
# M = 3
# N = 3
#
# # X(1) X(2) X(3) Degree
# +------------------------
# 1 | 0 0 0 0
# |
# 2 | 0 0 1 1
# 3 | 0 1 0 1
# 4 | 1 0 0 1
# |
# 5 | 0 0 2 2
# 6 | 0 1 1 2
# 7 | 1 0 1 2
# 8 | 0 2 0 2
# 9 | 1 1 0 2
# 10 | 2 0 0 2
# |
# 11 | 0 0 3 3
# 12 | 0 1 2 3
# 13 | 1 0 2 3
# 14 | 0 2 1 3
# 15 | 1 1 1 3
# 16 | 2 0 1 3
# 17 | 0 3 0 3
# 18 | 1 2 0 3
# 19 | 2 1 0 3
# 20 | 3 0 0 3
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 24 October 2014
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer M, the spatial dimension.
#
# Input, integer N, the total degree.
# 0 <= N.
#
# Input, integer X[M], the current monomial.
# The first element is X = [ 0, 0, ..., 0, 0 ].
# The last is [ N, 0, ..., 0, 0 ].
#
# Output, integer X[M], the next monomial.
#
from i4vec_sum import i4vec_sum
from mono_next_grevlex import mono_next_grevlex
if ( n < 0 ):
print ''
print 'MONO_UPTO_NEXT_GREVLEX - Fatal error!'
print ' N < 0.'
sys.exit ( 'MONO_UPTO_NEXT_GREVLEX - Fatal error!' )
if ( i4vec_sum ( m, x ) < 0 ):
print ''
print 'MONO_UPTO_NEXT_GREVLEX - Fatal error!'
print ' Input X sum is less than 0.'
sys.exit ( 'MONO_UPTO_NEXT_GREVLEX - Fatal error!' )
if ( n < i4vec_sum ( m, x ) ):
print ''
print 'MONO_UPTO_NEXT_GREVLEX - Fatal error!'
print ' Input X sum is more than N.'
sys.exit ( 'MONO_UPTO_NEXT_GREVLEX - Fatal error!' )
if ( n == 0 ):
return x
if ( x[0] == n ):
x[0] = 0
else:
x = mono_next_grevlex ( m, x )
return x
def mono_upto_next_grevlex(m, n, x):
#*****************************************************************************80
#
## MONO_UPTO_NEXT_GREVLEX: grevlex next monomial, total degree up to N.
#
# Discussion:
#
# We consider all monomials in an M-dimensional space, with total
# degree N.
#
# For example:
#
# M = 3
# N = 3
#
# # X(1) X(2) X(3) Degree
# +------------------------
# 1 | 0 0 0 0
# |
# 2 | 0 0 1 1
# 3 | 0 1 0 1
# 4 | 1 0 0 1
# |
# 5 | 0 0 2 2
# 6 | 0 1 1 2
# 7 | 1 0 1 2
# 8 | 0 2 0 2
# 9 | 1 1 0 2
# 10 | 2 0 0 2
# |
# 11 | 0 0 3 3
# 12 | 0 1 2 3
# 13 | 1 0 2 3
# 14 | 0 2 1 3
# 15 | 1 1 1 3
# 16 | 2 0 1 3
# 17 | 0 3 0 3
# 18 | 1 2 0 3
# 19 | 2 1 0 3
# 20 | 3 0 0 3
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 24 October 2014
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer M, the spatial dimension.
#
# Input, integer N, the total degree.
# 0 <= N.
#
# Input, integer X[M], the current monomial.
# The first element is X = [ 0, 0, ..., 0, 0 ].
# The last is [ N, 0, ..., 0, 0 ].
#
# Output, integer X[M], the next monomial.
#
from i4vec_sum import i4vec_sum
from mono_next_grevlex import mono_next_grevlex
if (n < 0):
print ''
print 'MONO_UPTO_NEXT_GREVLEX - Fatal error!'
print ' N < 0.'
sys.exit('MONO_UPTO_NEXT_GREVLEX - Fatal error!')
if (i4vec_sum(m, x) < 0):
print ''
print 'MONO_UPTO_NEXT_GREVLEX - Fatal error!'
print ' Input X sum is less than 0.'
sys.exit('MONO_UPTO_NEXT_GREVLEX - Fatal error!')
if (n < i4vec_sum(m, x)):
print ''
print 'MONO_UPTO_NEXT_GREVLEX - Fatal error!'
print ' Input X sum is more than N.'
sys.exit('MONO_UPTO_NEXT_GREVLEX - Fatal error!')
if (n == 0):
return x
if (x[0] == n):
x[0] = 0
else:
x = mono_next_grevlex(m, x)
return x
def mono_between_next_grevlex(m, n1, n2, x):
#*****************************************************************************80
#
## MONO_BETWEEN_NEXT_GREVLEX: grevlex next monomial, degree between N1 and N2.
#
# Discussion:
#
# We consider all monomials in an M-dimensional space, with total
# degree N between N1 and N2, inclusive.
#
# For example:
#
# M = 3
# N1 = 2
# N2 = 3
#
# # X(1) X(2) X(3) Degree
# +------------------------
# 1 | 0 0 2 2
# 2 | 0 1 1 2
# 3 | 1 0 1 2
# 4 | 0 2 0 2
# 5 | 1 1 0 2
# 6 | 2 0 0 2
# |
# 7 | 0 0 3 3
# 8 | 0 1 2 3
# 9 | 1 0 2 3
# 10 | 0 2 1 3
# 11 | 1 1 1 3
# 12 | 2 0 1 3
# 13 | 0 3 0 3
# 14 | 1 2 0 3
# 15 | 2 1 0 3
# 16 | 3 0 0 3
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 24 October 2014
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer M, the spatial dimension.
#
# Input, integer N1, N2, the minimum and maximum degrees.
# 0 <= N1 <= N2.
#
# Input, integer X[M], the current monomial.
# The first element is X = [ 0, 0, ..., 0, N1 ].
# The last is [ N2, 0, ..., 0, 0 ].
#
# Output, integer X[M], the next monomial.
#
from i4vec_sum import i4vec_sum
from mono_next_grevlex import mono_next_grevlex
if (n1 < 0):
print ''
print 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!'
print ' N1 < 0.'
sys.exit('MONO_BETWEEN_NEXT_GREVLEX - Fatal error!')
if (n2 < n1):
print ''
print 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!'
print ' N2 < N1.'
sys.exit('MONO_BETWEEN_NEXT_GREVLEX - Fatal error!')
if (i4vec_sum(m, x) < n1):
print ''
print 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!'
print ' Input X sums to less than N1.'
sys.exit('MONO_BETWEEN_NEXT_GREVLEX - Fatal error!')
if (n2 < i4vec_sum(m, x)):
print ''
print 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!'
print ' Input X sums to more than N2.'
sys.exit('MONO_BETWEEN_NEXT_GREVLEX - Fatal error!')
if (n2 == 0):
return x
if (x[0] == n2):
x[0] = 0
x[m - 1] = n1
else:
x = mono_next_grevlex(m, x)
return x
def mono_between_next_grevlex ( m, n1, n2, x ):
#*****************************************************************************80
#
## MONO_BETWEEN_NEXT_GREVLEX: grevlex next monomial, degree between N1 and N2.
#
# Discussion:
#
# We consider all monomials in an M-dimensional space, with total
# degree N between N1 and N2, inclusive.
#
# For example:
#
# M = 3
# N1 = 2
# N2 = 3
#
# # X(1) X(2) X(3) Degree
# +------------------------
# 1 | 0 0 2 2
# 2 | 0 1 1 2
# 3 | 1 0 1 2
# 4 | 0 2 0 2
# 5 | 1 1 0 2
# 6 | 2 0 0 2
# |
# 7 | 0 0 3 3
# 8 | 0 1 2 3
# 9 | 1 0 2 3
# 10 | 0 2 1 3
# 11 | 1 1 1 3
# 12 | 2 0 1 3
# 13 | 0 3 0 3
# 14 | 1 2 0 3
# 15 | 2 1 0 3
# 16 | 3 0 0 3
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 24 October 2014
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer M, the spatial dimension.
#
# Input, integer N1, N2, the minimum and maximum degrees.
# 0 <= N1 <= N2.
#
# Input, integer X[M], the current monomial.
# The first element is X = [ 0, 0, ..., 0, N1 ].
# The last is [ N2, 0, ..., 0, 0 ].
#
# Output, integer X[M], the next monomial.
#
from i4vec_sum import i4vec_sum
from mono_next_grevlex import mono_next_grevlex
if ( n1 < 0 ):
print ''
print 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!'
print ' N1 < 0.'
sys.exit ( 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!' )
if ( n2 < n1 ):
print ''
print 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!'
print ' N2 < N1.'
sys.exit ( 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!' )
if ( i4vec_sum ( m, x ) < n1 ):
print ''
print 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!'
print ' Input X sums to less than N1.'
sys.exit ( 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!' )
if ( n2 < i4vec_sum ( m, x ) ):
print ''
print 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!'
print ' Input X sums to more than N2.'
sys.exit ( 'MONO_BETWEEN_NEXT_GREVLEX - Fatal error!' )
if ( n2 == 0 ):
return x
if ( x[0] == n2 ):
x[0] = 0
x[m-1] = n1
else:
x = mono_next_grevlex ( m, x )
return x