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* Polynomial.lc() instead of .lead() (.lead() still exists as alias)
* Polynomial.cc() instead of .c() (.c() still exists as alias)
* Minor adjustments
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@foo123
foo123 committed Jan 26, 2020
1 parent 126ccfc commit 23a490d
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Showing 3 changed files with 37 additions and 45 deletions.
67 changes: 37 additions & 30 deletions src/js/Abacus.js
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Original file line number Diff line number Diff line change
Expand Up @@ -2565,28 +2565,28 @@ function polygcd( /* args */ )
}
}
// defer to integer gcd and transform back to polynomial
if ( are_const ) return Polynomial(gcd(slice.call(args).map(function(p){return p.c().num;})), args[0].symbol);
if ( are_const ) return Polynomial(gcd(slice.call(args).map(function(p){return p.cc().num;})), args[0].symbol);

/*for(i=0; i<c; i++)
{
if ( args[i].lead().lt(O) ) args[i] = args[i].neg();
if ( args[i].lc().lt(O) ) args[i] = args[i].neg();
if ( args[i].equ(O) ) zeroes++;
}
if ( zeroes === c ) return Polynomial([], args[0].symbol);*/
i = 0;
while(i<c && (a=args[i++]).equ(O)) ;
if ( a.lead().lt(O) ) a = a.neg();
if ( a.lc().lt(O) ) a = a.neg();
while (i<c)
{
if ( a.equ(I) ) return Polynomial(I, a.symbol);
while(i<c && (b=args[i++]).equ(O)) ;
if ( b.lead().lt(O) ) b = b.neg();
if ( b.lc().lt(O) ) b = b.neg();
if ( b.equ(I) ) return Polynomial(I, a.symbol);
else if ( b.equ(a) ) continue;
else if ( b.equ(O) ) break;
// swap them (a >= b)
if ( (a.deg() < b.deg()) ||
((a.deg() === b.deg()) && a.lead().lt(b.lead())) ) { t=b; b=a; a=t; }
((a.deg() === b.deg()) && a.lc().lt(b.lc())) ) { t=b; b=a; a=t; }
while ( !b.equ(O) /*0 < b.deg()*/)
{
a0 = a; b0 = b;
Expand All @@ -2595,8 +2595,8 @@ function polygcd( /* args */ )
}
}
// simplify, positive and monic
if ( a.lead().lt(O) ) a = a.neg();
if ( !a.lead().equ(I) ) a = a.div(a.lead());
if ( a.lc().lt(O) ) a = a.neg();
if ( !a.lc().equ(I) ) a = a.div(a.lc());
return a;
}
function polylcm2( a, b )
Expand Down Expand Up @@ -2642,7 +2642,7 @@ function polyxgcd( /* args */ )
}
}
// defer to integer gcd and transform back to polynomial
if ( are_const ) return xgcd(slice.call(args).map(function(p){return p.c().num;})).map(function(g){return Polynomial(g, args[0].symbol);});
if ( are_const ) return xgcd(slice.call(args).map(function(p){return p.cc().num;})).map(function(g){return Polynomial(g, args[0].symbol);});

a = args[0];

Expand All @@ -2651,10 +2651,10 @@ function polyxgcd( /* args */ )
a2 = Polynomial(O, a.symbol);
b2 = Polynomial(I, a.symbol);

if ( a.lead().lt(O) ) {a = a.neg(); asign = asign.neg();}
if ( a.lc().lt(O) ) {a = a.neg(); asign = asign.neg();}
if ( 1 === k )
{
if ( !a.lead().equ(I) ) {lead = a.lead(); a = a.div(lead); asign = asign.div(lead);}
if ( !a.lc().equ(I) ) {lead = a.lc(); a = a.div(lead); asign = asign.div(lead);}
return [a, Polynomial(asign, a.symbol)];
}
else //if ( 2 <= k )
Expand All @@ -2670,19 +2670,19 @@ function polyxgcd( /* args */ )
// note3: gcd(0,0,..,0) is conventionaly set to 0 with 1's as factors
xgcdp = 2===k ? [args[1], Polynomial(I, a.symbol)] : polyxgcd(slice.call(args, 1));
b = xgcdp[0];
if ( b.lead().lt(O) ) {b = b.neg(); bsign = bsign.neg();}
if ( b.lc().lt(O) ) {b = b.neg(); bsign = bsign.neg();}

// gcd with zero factor, take into account
if ( a.equ(O) )
{
if ( !b.lead().equ(I) ) {lead = b.lead(); b = b.div(lead); asign = asign.div(lead); bsign = bsign.div(lead);}
if ( !b.lc().equ(I) ) {lead = b.lc(); b = b.div(lead); asign = asign.div(lead); bsign = bsign.div(lead);}
return array(xgcdp.length+1,function(i){
return 0===i ? b : (1===i ? Polynomial(asign, a.symbol) : xgcdp[i-1].mul(bsign));
});
}
else if ( b.equ(O) )
{
if ( !a.lead().equ(I) ) {lead = a.lead(); a = a.div(lead); asign = asign.div(lead); bsign = bsign.div(lead);}
if ( !a.lc().equ(I) ) {lead = a.lc(); a = a.div(lead); asign = asign.div(lead); bsign = bsign.div(lead);}
return array(xgcdp.length+1,function(i){
return 0===i ? a : (1===i ? Polynomial(asign, a.symbol) : xgcdp[i-1].mul(bsign));
});
Expand All @@ -2698,8 +2698,8 @@ function polyxgcd( /* args */ )
b1 = b1.sub(qr[0].mul(b2));
if ( a.equ(O) /*0 === a.deg()*/ )
{
if ( b.lead().lt(O) ) {b = b.neg(); asign = asign.neg(); bsign = bsign.neg();}
if ( !b.lead().equ(I) ) {lead = b.lead(); b = b.div(lead); asign = asign.div(lead); bsign = bsign.div(lead);}
if ( b.lc().lt(O) ) {b = b.neg(); asign = asign.neg(); bsign = bsign.neg();}
if ( !b.lc().equ(I) ) {lead = b.lc(); b = b.div(lead); asign = asign.div(lead); bsign = bsign.div(lead);}
a2 = a2.mul(asign); b2 = b2.mul(bsign);
return array(xgcdp.length+1,function(i){
return 0===i ? b : (1===i ? a2 : xgcdp[i-1].mul(b2));
Expand All @@ -2712,8 +2712,8 @@ function polyxgcd( /* args */ )
b2 = b2.sub(qr[0].mul(b1));
if( b.equ(O) /*0 === b.deg()*/ )
{
if ( a.lead().lt(O) ) {a = a.neg(); asign = asign.neg(); bsign = bsign.neg();}
if ( !a.lead().equ(I) ) {lead = a.lead(); a = a.div(lead); asign = asign.div(lead); bsign = bsign.div(lead);}
if ( a.lc().lt(O) ) {a = a.neg(); asign = asign.neg(); bsign = bsign.neg();}
if ( !a.lc().equ(I) ) {lead = a.lc(); a = a.div(lead); asign = asign.div(lead); bsign = bsign.div(lead);}
a1 = a1.mul(asign); b1 = b1.mul(bsign);
return array(xgcdp.length+1, function(i){
return 0===i ? a : (1===i ? a1 : xgcdp[i-1].mul(b1));
Expand All @@ -2723,8 +2723,8 @@ function polyxgcd( /* args */ )
if ( a.equ(a0) && b.equ(b0) )
{
// will not change anymore
if ( a.lead().lt(O) ) {a = a.neg(); asign = asign.neg(); bsign = bsign.neg();}
if ( !a.lead().equ(I) ) {lead = a.lead(); a = a.div(lead); asign = asign.div(lead); bsign = bsign.div(lead);}
if ( a.lc().lt(O) ) {a = a.neg(); asign = asign.neg(); bsign = bsign.neg();}
if ( !a.lc().equ(I) ) {lead = a.lc(); a = a.div(lead); asign = asign.div(lead); bsign = bsign.div(lead);}
a1 = a1.mul(asign); b1 = b1.mul(bsign);
return array(xgcdp.length+1, function(i){
return 0===i ? a : (1===i ? a1 : xgcdp[i-1].mul(b1));
Expand Down Expand Up @@ -2762,7 +2762,7 @@ function polyfactorize( p )
remainder = remainder.mul(m);
}
if ( 0 < remainder.deg() ) factors.push([remainder, 1]);
else constant = constant.mul(remainder.c());
else constant = constant.mul(remainder.cc());
}
if ( !factors.length ) factors.push([Polynomial(Arithmetic.I, p.symbol), 1]);
return [factors, constant];
Expand Down Expand Up @@ -7455,7 +7455,6 @@ Expr = Abacus.Expr = Class(INumber, {
}
sign = m[1] || '';
// accept only real coefficients, not complex for now
console.log([symbol, coeff]);
n = /\\frac/.test(coeff) ? Rational.fromTex(sign+coeff) : Rational.fromString(sign+coeff);
if ( !n ) continue;
terms.push(Term(symbol, n));
Expand Down Expand Up @@ -8084,16 +8083,24 @@ Polynomial = Abacus.Polynomial = Class(INumber, {
var coeff = this.coeff;
return coeff.length ? coeff[0].e : 0;
}
,lead: function( ) {
,lc: function( ) {
// leading coefficient
var coeff = this.coeff;
return coeff.length ? coeff[0].c : Rational.ZERO();
}
,c: function( ) {
,cc: function( ) {
// constant coefficient
var coeff = this.coeff;
return coeff.length ? coeff[coeff.length-1].c : Rational.ZERO();
}
,lead: function( ) {
// alias of lc()
return this.lc();
}
,c: function( ) {
// alias of cc()
return this.cc();
}
,primitive: function( and_content ) {
// factorise into content and primitive part
// https://en.wikipedia.org/wiki/Factorization_of_polynomials#Primitive_part%E2%80%93content_factorization
Expand Down Expand Up @@ -8225,7 +8232,7 @@ Polynomial = Abacus.Polynomial = Class(INumber, {
var self = this, Arithmetic = Abacus.Arithmetic;
if ( (a instanceof Complex) || (a instanceof Rational) || Arithmetic.isNumber(a) )
{
return 0 < self.deg() ? false : self.c().gt(a);
return 0 < self.deg() ? false : self.cc().gt(a);
}
else if ( a instanceof Polynomial )
{
Expand All @@ -8241,7 +8248,7 @@ Polynomial = Abacus.Polynomial = Class(INumber, {
var self = this, Arithmetic = Abacus.Arithmetic;
if ( (a instanceof Complex) || (a instanceof Rational) || Arithmetic.isNumber(a) )
{
return 0 < self.deg() ? false : self.c().gte(a);
return 0 < self.deg() ? false : self.cc().gte(a);
}
else if ( a instanceof Polynomial )
{
Expand All @@ -8257,7 +8264,7 @@ Polynomial = Abacus.Polynomial = Class(INumber, {
var self = this, Arithmetic = Abacus.Arithmetic;
if ( (a instanceof Complex) || (a instanceof Rational) || Arithmetic.isNumber(a) )
{
return 0 < self.deg() ? false : self.c().lt(a);
return 0 < self.deg() ? false : self.cc().lt(a);
}
else if ( a instanceof Polynomial )
{
Expand All @@ -8273,7 +8280,7 @@ Polynomial = Abacus.Polynomial = Class(INumber, {
var self = this, Arithmetic = Abacus.Arithmetic;
if ( (a instanceof Complex) || (a instanceof Rational) || Arithmetic.isNumber(a) )
{
return 0 < self.deg() ? false : self.c().lte(a);
return 0 < self.deg() ? false : self.cc().lte(a);
}
else if ( a instanceof Polynomial )
{
Expand Down Expand Up @@ -8331,7 +8338,7 @@ Polynomial = Abacus.Polynomial = Class(INumber, {
if ( 0 === x.deg() )
{
// constant polynomial, simple numeric division
x = x.c();
x = x.cc();
q = x.equ(I) ? Polynomial(self) : Polynomial(array(self.coeff.length, function(i){
return Coeff(self.coeff[i].c.div(x), self.coeff[i].e);
}), self.symbol);
Expand All @@ -8348,7 +8355,7 @@ Polynomial = Abacus.Polynomial = Class(INumber, {
{
diff0 = diff;
d = x.shift(diff);
q[diff] = r.lead().div(d.lead());
q[diff] = r.lc().div(d.lc());
r = Polynomial.Add(Polynomial.Mul(q[diff], d), r, true);
diff = r.deg()-x.deg();
if ( (diff === diff0) ) break; // remainder won't change anymore
Expand Down Expand Up @@ -8418,7 +8425,7 @@ Polynomial = Abacus.Polynomial = Class(INumber, {
// also check http://andy.novocin.com/pro/polycomp_CASC2011.pdf
if ( !self.coeff.length ) return Polynomial([], q.symbol);
if ( 0 === self.deg() ) return Polynomial(self.coeff.slice(), q.symbol);
if ( 0 === q.deg() ) return Polynomial(self.valueOf(q.c()), q.symbol);
if ( 0 === q.deg() ) return Polynomial(self.valueOf(q.cc()), q.symbol);
c = self.coeff;
i = c[0].e; pq = Polynomial(c[0].c, q.symbol); j = 1;
while(0<i)
Expand Down
4 changes: 0 additions & 4 deletions test/expressions.txt
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Original file line number Diff line number Diff line change
Expand Up @@ -14,12 +14,8 @@ o.d("x")
o.dispose()
---
Abacus.Expr.fromString("1+2*x").toString()
[ '1', '1' ]
[ 'x', '2' ]
1+2*x
Abacus.Expr.fromString("1/2+2*x_{1}*x_2^2").toString()
[ '1', '1/2' ]
[ 'x_{1}*x_2^2', '2' ]
1/2+2*x_1*x_2^2
---
o=Abacus.Expr(1, Abacus.Term("x", 2))
Expand Down
11 changes: 0 additions & 11 deletions test/polynomials.txt
View file
Original file line number Diff line number Diff line change
Expand Up @@ -34,25 +34,14 @@ x^50+2*x^2
o.dispose()
---
Abacus.Polynomial.fromString("1").toString()
[ '1', '0' ]
1
Abacus.Polynomial.fromString("1 + x^2").toString()
[ '1', '0' ]
[ '1', '2' ]
x^2+1
Abacus.Polynomial.fromString("1 - x^2").toString()
[ '1', '0' ]
[ '1', '2' ]
-x^2+1
Abacus.Polynomial.fromString("1 - (2/3)*x^2+x").toString()
[ '1', '0' ]
[ '(2/3)', '2' ]
[ '1', '1' ]
-(2/3)*x^2+x+1
Abacus.Polynomial.fromString("1 - \frac{2}{3}*x^{2}+x").toString()
[ '1', '0' ]
[ '\\frac{2}{3}', '2' ]
[ '1', '1' ]
-(2/3)*x^2+x+1
---
o=Abacus.Polynomial([2,0,1])
Expand Down

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