class POLYS_INTI < $IS_LT{POLYS_INTI},$STR


Ancestors
$STR $IS_LT{_} $IS_EQ



Public


Readable Attributes
attr arr: ARRAY{R}; .. Included as arr

Writable Attributes
attr arr: ARRAY{R}; .. Included as arr

Readonly Shareds
shared divmodForce0:BOOL; .. Included as divmodForce0
shared r_0:R; .. Included as r_0
shared r_1:R; .. Included as r_1

Writable Shareds
shared divmodForce0:BOOL; .. Included as divmodForce0
shared r_0:R; .. Included as r_0
shared r_1:R; .. Included as r_1

Features
is_SqrFree:BOOL .. Included as POLYS_is_SqrFree
squareFreeDecomposition:ARRAY{SAME} .. Included as POLYS_squareFreeDecomposition
S_poly_PID(g:SAME):SAME
S_poly_PID_L2(g:SAME):SAME
**** S in Z<x>. Erase lowest term.
S_poly_PID_L3(g:SAME):SAME
**** S in Z<x>
aget(i:INT): R .. Included as aget
allocate(d:INT):SAME .. Included as allocate
**** degree "d"
array:ARRAY{R} .. Included as array
aset(i:INT, v:R) .. Included as aset
clear .. Included as clear
compare(other:SAME):INT .. Included as compare
**** <=>: -1 if "<", 0 if "=", 1 if ">" .
constructionHensel(g,h:SAME, n,prime,pn:INTI, out g1,out h1:SAME)
**** Hensel's construction. Input: self,g,h,n,prime,pn s.t. self==g*h (mod pn), pn=prime^n Output: g,h s.t. f=g*h (mod prime^(n+1))
copy:SAME .. Included as copy
countSolution(a,b:INTI , countRedundancy:BOOL):INT
create(a:ARRAY{R}):SAME .. Included as create
create(c:R): SAME .. Included as create
**** same as create(c,0)
create(c:R,d:INT): SAME .. Included as create
**** c*x^(d)
create: SAME .. Included as create
**** same as create(r_0,c)
deep_copy:SAME .. Included as deep_copy
degree:INT .. Included as degree
derivative(n:INT):SAME .. Included as derivative
**** n-th derivative
derivative:SAME .. Included as derivative
div(other:SAME): SAME .. Included as div
divmod(force0:BOOL, divisor:SAME, out q:SAME, out r:SAME) .. Included as divmod
**** R be field or PID "force0" be true to force "0" at head of remainder. true: continuous field e.g.FLT,FLTD, CPX,CPXD... false: PID or discrete field or RAT e.g. INT,INTI,RAT,finite field
divmod(divisor:SAME, out q:SAME, out r:SAME) .. Included as divmod
divmod_Zp(p:INTI, divisor:SAME, out q:SAME, out r:SAME)
**** as Zp coefficient polynomial.
evenly_divides(o:SAME):BOOL .. Included as evenly_divides
****
__self|o._True_if_self_evenly_divides_`o'.
exp_gen_func(a:ARRAY{R}):SAME .. Included as exp_gen_func
**** exponential generating function
extended_gcd(a:ARRAY{SAME},out factor:ARRAY{SAME}):SAME .. Included as extended_gcd
**** multi GCD. return GCD g. g = a . factor
extended_gcd(o:SAME,out f1: SAME, out f2:SAME):SAME .. Included as extended_gcd
**** gcd = self*f1 + o*f2
extended_gcd_Zp(prime:INTI,o:SAME, out f1:SAME, out f2:SAME):SAME
factorize:ARRAY{SAME}
gcd(a:ARRAY{SAME}):SAME .. Included as gcd
**** multi GCD. return GCD of elements of a[].
gcd(o:SAME):SAME .. Included as gcd
gcd_Zp(prime:INTI, o:SAME):SAME
**** Euclidean algorithm.
gcd_coeff:INTI
**** gcd of coefficients
gen_func(a:ARRAY{R}):SAME .. Included as gen_func
**** generating function.
init
integral(n:INT):SAME .. Included as integral
**** integral n-times
integral:SAME .. Included as integral
is_SqrFree(prime:INTI):BOOL
is_SqrFree:BOOL
is_eq(other:SAME): BOOL .. Included as is_eq
.. Included as is_eq
is_lt(other:SAME): BOOL .. Included as is_lt
****
____expr1_<_expr2_____expr1.is_lt(expr2)
return degree<other.degree;
is_one:BOOL .. Included as is_one
is_zero: BOOL .. Included as is_zero
lc: R .. Included as lc
**** lc: leading coefficient
lcm(o:SAME):SAME .. Included as lcm
lcm_coeff:INTI
**** lcm of of coefficients
low_deg:INT .. Included as low_deg
**** (lowest degree of non-zero term) or 0.
lp:SAME .. Included as lp
**** leading power product
lt:SAME .. Included as lt
**** leading term
mindeg:INT .. Included as mindeg
**** minimum degree of non-zero term
minus(other:INT):SAME .. Included as minus
minus(other:R):SAME .. Included as minus
minus(other:SAME):SAME .. Included as minus
mod(other:ARRAY{SAME}):SAME .. Included as mod
**** mod for multi division
mod(n:INTI):SAME
**** mod for each coeff.
mod(other:SAME): SAME .. Included as mod
mod_lt(other:ARRAY{SAME}):SAME
**** mod for leading term
mod_n(n:INTI):SAME
**** mod( -n/2< coeff <= n/2 ) for each coeff.
monic .. Included as monic
**** make monic i.e. f(x/lc)*(lc^(degree-1))
negate:SAME .. Included as negate
normalize .. Included as normalize
**** destructive. ### Note that arr[0]==0 for polynomial "0".
normalize:SAME .. Included as normalize
one:SAME .. Included as one
plus(other:INT):SAME .. Included as plus
plus(other:R):SAME .. Included as plus
plus(other:SAME):SAME .. Included as plus
polys_rat:POLYS_RAT
pow(power:INT): SAME .. Included as pow
pow(power:INTI): SAME .. Included as pow
pseudo_monic(c:R) .. Included as pseudo_monic
**** f(x/c)*(c^degree)
remove_gcd
**** self/gcd_coeff
remove_gcd:SAME
**** self/gcd_coeff
reverseDeg:SAME .. Included as reverseDeg
shift0:SAME .. Included as shift0
shift_deg(d:INT):SAME .. Included as shift_deg
**** self * (x^d)
squareFreeDecomposition:ARRAY{SAME}
str(format:STR, v:STR, r:BOOL): STR .. Included as str
**** needed "is_lt" in R. format: "text","tex", "texm", "prog" v: variable, r: switch of order. true:decreasing order. false:increasing order
str:STR .. Included as str
substitute(x:R):R .. Included as substitute
substitute(x:SAME):SAME .. Included as substitute
times(other:INT):SAME .. Included as times
times(other:R):SAME .. Included as times
times(other:SAME): SAME .. Included as times
x:SAME .. Included as x
zero:SAME .. Included as zero

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