<poly_test.awl> {

<polynom.awl> <- <poly_test.awl> {


} <polynom.awl> #182 / [13]

Imported 'polynom.awl'...

Class 'poly' (members):

    List;
    Rank;


Class 'poly' (functors):

    ! poly.sub:(P Q) [5] = {
      set:((m, n), with:(P, poly.Rank), with:(Q, poly.Rank));
      if:(le:(m, n), with:(Q, while:(gt:(n, m), l_push:(Res, neg:l_item:(dec_p:n, poly.List)))), with:(P, while:(gt:(m, n), l_push:(Res, l_item:(dec_p:m, poly.List)))));
      while:(ge:(n, 0), {
	l_push:(Res, sub:(with:(P, l_item:(n, poly.List)), with:(Q, l_item:(n, poly.List))));
	dec:n });
      .poly:Res };
    ! poly.combine:(P Q) [8] = {
      set:((nP, nQ), with:(P, poly.Rank), with:(Q, poly.Rank));
      set:(Res, l_rep:(add:(mul:(nP, nQ), 1), 0));
      with:(P, for_inc:(i, add:(nP, 1), {
	set:(V, l_item:(i, poly.List));
	with:(poly.power:(Q, i), for_inc:(j, add:(mul:(nQ, i), 1), comb:add:(l_item:(j, Res), mul:(l_item:(j, poly.List), V)))) }));
      .poly:Res };
    ! poly.cmp:(P Q) [4] = {
      set:((m, n), with:(P, poly.Rank), with:(Q, poly.Rank));
      if:(ne:(m, n), cmp:(m, n), {
	while:(c_and:(ge:(n, 0), eq:(with:(P, l_item:(n, poly.List)), with:(Q, l_item:(n, poly.List)))), dec:n);
	if:(ge:(n, 0), cmp:(with:(P, l_item:(n, poly.List)), with:(Q, l_item:(n, poly.List))), 0);
	}) };
    ! poly.binomial:(N) [6] = {
      for_inc:(p, add:(N, 1), {
	set:(pN, set:(pD, 1));
	for_inc:(n, p, {
	  comb:mul:(pN, sub:(N, n));
	  comb:mul:(pD, add:(n, 1)) });
	l_push:(Res, idiv:(pN, pD)) });
      .poly:Res };
    ! poly.neg:(P) [3] = {
      set:(n, with:(P, poly.Rank));
      with:(P, while:(ge:(n, 0), l_push:(Res, neg:l_item:(dec_p:n, poly.List))));
      .poly:Res };
    ! poly.div:(P Q) [9] = {
      set:((nP, nQ), with:(P, poly.Rank), with:(Q, poly.Rank));
      set:(Rem, l_copy:with:(P, poly.List));
      set:(D, with:(Q, l_item:(nQ, poly.List)));
      while:(ge:(nP, nQ), {
	set:(F, div:(l_item:(nP, Rem), D));
	set:(l_item:(nP, Rem), 0);
	l_push:(Quot, F);
	with:(Q, for_inc:(i, (1, add:(nQ, 1)), comb:sub:(l_item:(sub:(nP, i), Rem), mul:(l_item:(sub:(nQ, i), poly.List), F))));
	dec:nP });
      (.poly:Quot, .poly:Rem) };
    ! poly.power:(P n) [3] = {
      if:(n, {
	set:(Res, P);
	while:(dec:n, set:(Res, poly.mul:(Res, P)));
	Res }, .poly:1) };
    ! poly.add:(P Q) [5] = {
      set:((m, n), with:(P, poly.Rank), with:(Q, poly.Rank));
      with:(if:(le:(m, n), Q, {
	swap:(m, n);
	P }), while:(gt:(n, m), l_push:(Res, l_item:(dec_p:n, poly.List))));
      while:(ge:(n, 0), {
	l_push:(Res, add:(with:(P, l_item:(n, poly.List)), with:(Q, l_item:(n, poly.List))));
	dec:n });
      .poly:Res };
    ! poly.put:(X) [3] = {
      set:(n, poly.Rank);
      if:(lt:(n, 0), f_put:((), 0), do_while:(ge:(dec:n, 0), {
	set:(val, l_item:(n, poly.List));
	if:(ne:(n, poly.Rank), if:(gt:(val, 0), f_put:((), " + ", val), if:(lt:(val, 0), f_put:((), " - ", neg:val))), if:(ne:(val, 1), f_put:((), val)));
	if:(gt:(n, 0), {
	  f_put:((), X);
	  if:(gt:(n, 1), f_put:((), "^", n));
	  });
	}));
      };
    ! poly.eval:(X) [3] = {
      set:(n, poly.Rank);
      set:(val, 0);
      while:(ge:(n, 0), {
	comb:add:(val, l_item:(dec_p:n, poly.List));
	if:(ge:(n, 0), comb:mul:(val, X)) });
      val };
    ! poly.mul:(P Q) [8] = {
      set:((nP, nQ), with:(P, poly.Rank), with:(Q, poly.Rank));
      for_dec:(n, add:(add:(nP, nQ), 1), {
	set:(C, 0);
	for_inc:(i, add:(n, 1), if:(c_and:(le:(i, nP), le:(sub:(n, i), nQ)), comb:add:(C, mul:(with:(P, l_item:(i, poly.List)), with:(Q, l_item:(sub:(n, i), poly.List))))));
	l_push:(Res, C) });
      .poly:Res };


p_test1 = 95x + 37
p_test2 = 33x^2 + 22x + 12
p_test3 = 17x^3 + 35x^2 + 61x + 14

TESTING: evaluation...

(95x + 37) [5] = 512
(95x + 37) [-5] = -438
(33x^2 + 22x + 12) [10] = 3532
(33x^2 + 22x + 12) [-10] = 3092
(17x^3 + 35x^2 + 61x + 14) [4] = 1906
(17x^3 + 35x^2 + 61x + 14) [-4] = -758

TESTING: polynoms negation...

-(95x + 37) = -95x - 37
-(-(95x + 37)) = 95x + 37

-(33x^2 + 22x + 12) = -33x^2 - 22x - 12
-(-(33x^2 + 22x + 12)) = 33x^2 + 22x + 12

-(17x^3 + 35x^2 + 61x + 14) = -17x^3 - 35x^2 - 61x - 14
-(-(17x^3 + 35x^2 + 61x + 14)) = 17x^3 + 35x^2 + 61x + 14


TESTING: polynoms addition commutativity...

(95x + 37) + (33x^2 + 22x + 12) = 33x^2 + 117x + 49
(33x^2 + 22x + 12) + (95x + 37) = 33x^2 + 117x + 49

(33x^2 + 22x + 12) + (17x^3 + 35x^2 + 61x + 14) = 17x^3 + 68x^2 + 83x + 26
(17x^3 + 35x^2 + 61x + 14) + (33x^2 + 22x + 12) = 17x^3 + 68x^2 + 83x + 26

(17x^3 + 35x^2 + 61x + 14) + (95x + 37) = 17x^3 + 35x^2 + 156x + 51
(95x + 37) + (17x^3 + 35x^2 + 61x + 14) = 17x^3 + 35x^2 + 156x + 51


TESTING: polynoms subtraction anticommutativity...

(95x + 37) - (33x^2 + 22x + 12) = -33x^2 + 73x + 25
-((33x^2 + 22x + 12) - (95x + 37)) = -33x^2 + 73x + 25

(33x^2 + 22x + 12) - (17x^3 + 35x^2 + 61x + 14) = -17x^3 - 2x^2 - 39x - 2
-((17x^3 + 35x^2 + 61x + 14) - (33x^2 + 22x + 12)) = -17x^3 - 2x^2 - 39x - 2

(17x^3 + 35x^2 + 61x + 14) - (95x + 37) = 17x^3 + 35x^2 - 34x - 23
-((95x + 37) - (17x^3 + 35x^2 + 61x + 14)) = 17x^3 + 35x^2 - 34x - 23


TESTING: polynoms addition associativity...

((95x + 37) + (33x^2 + 22x + 12)) + (17x^3 + 35x^2 + 61x + 14) = 17x^3 + 68x^2 + 178x + 63
(95x + 37) + ((33x^2 + 22x + 12) + (17x^3 + 35x^2 + 61x + 14)) = 17x^3 + 68x^2 + 178x + 63

((17x^3 + 35x^2 + 61x + 14) + (33x^2 + 22x + 12)) + (95x + 37) = 17x^3 + 68x^2 + 178x + 63
(17x^3 + 35x^2 + 61x + 14) + ((33x^2 + 22x + 12) + (95x + 37)) = 17x^3 + 68x^2 + 178x + 63


TESTING: polynoms multiplication commutativity...

(95x + 37) * (33x^2 + 22x + 12) = 3135x^3 + 3311x^2 + 1954x + 444
(33x^2 + 22x + 12) * (95x + 37) = 3135x^3 + 3311x^2 + 1954x + 444

(33x^2 + 22x + 12) * (17x^3 + 35x^2 + 61x + 14) = 561x^5 + 1529x^4 + 2987x^3 + 2224x^2 + 1040x + 168
(17x^3 + 35x^2 + 61x + 14) * (33x^2 + 22x + 12) = 561x^5 + 1529x^4 + 2987x^3 + 2224x^2 + 1040x + 168

(17x^3 + 35x^2 + 61x + 14) * (95x + 37) = 1615x^4 + 3954x^3 + 7090x^2 + 3587x + 518
(95x + 37) * (17x^3 + 35x^2 + 61x + 14) = 1615x^4 + 3954x^3 + 7090x^2 + 3587x + 518


TESTING: polynoms multiplication associativity...

((95x + 37) * (33x^2 + 22x + 12)) * (17x^3 + 35x^2 + 61x + 14) = 53295x^6 + 166012x^5 + 340338x^4 + 321799x^3 + 181088x^2 + 54440x + 6216
(95x + 37) * ((33x^2 + 22x + 12) * (17x^3 + 35x^2 + 61x + 14)) = 53295x^6 + 166012x^5 + 340338x^4 + 321799x^3 + 181088x^2 + 54440x + 6216

((33x^2 + 22x + 12) * (17x^3 + 35x^2 + 61x + 14)) * (95x + 37) = 53295x^6 + 166012x^5 + 340338x^4 + 321799x^3 + 181088x^2 + 54440x + 6216
(33x^2 + 22x + 12) * ((17x^3 + 35x^2 + 61x + 14) * (95x + 37)) = 53295x^6 + 166012x^5 + 340338x^4 + 321799x^3 + 181088x^2 + 54440x + 6216

((17x^3 + 35x^2 + 61x + 14) * (95x + 37)) * (33x^2 + 22x + 12) = 53295x^6 + 166012x^5 + 340338x^4 + 321799x^3 + 181088x^2 + 54440x + 6216
(17x^3 + 35x^2 + 61x + 14) * ((95x + 37) * (33x^2 + 22x + 12)) = 53295x^6 + 166012x^5 + 340338x^4 + 321799x^3 + 181088x^2 + 54440x + 6216


TESTING: polynoms multiplication distributivity...

((95x + 37) + (33x^2 + 22x + 12)) * (17x^3 + 35x^2 + 61x + 14) = 561x^5 + 3144x^4 + 6941x^3 + 9314x^2 + 4627x + 686
((95x + 37) * (17x^3 + 35x^2 + 61x + 14)) + ((33x^2 + 22x + 12) * (17x^3 + 35x^2 + 61x + 14)) = 561x^5 + 3144x^4 + 6941x^3 + 9314x^2 + 4627x + 686
((95x + 37) - (33x^2 + 22x + 12)) * (17x^3 + 35x^2 + 61x + 14) = -561x^5 + 86x^4 + 967x^3 + 4866x^2 + 2547x + 350
((95x + 37) * (17x^3 + 35x^2 + 61x + 14)) - ((33x^2 + 22x + 12) * (17x^3 + 35x^2 + 61x + 14)) = -561x^5 + 86x^4 + 967x^3 + 4866x^2 + 2547x + 350

((33x^2 + 22x + 12) + (17x^3 + 35x^2 + 61x + 14)) * (95x + 37) = 1615x^4 + 7089x^3 + 10401x^2 + 5541x + 962
((33x^2 + 22x + 12) * (95x + 37)) + ((17x^3 + 35x^2 + 61x + 14) * (95x + 37)) = 1615x^4 + 7089x^3 + 10401x^2 + 5541x + 962
((33x^2 + 22x + 12) - (17x^3 + 35x^2 + 61x + 14)) * (95x + 37) = -1615x^4 - 819x^3 - 3779x^2 - 1633x - 74
((33x^2 + 22x + 12) * (95x + 37)) - ((17x^3 + 35x^2 + 61x + 14) * (95x + 37)) = -1615x^4 - 819x^3 - 3779x^2 - 1633x - 74

((17x^3 + 35x^2 + 61x + 14) + (95x + 37)) * (33x^2 + 22x + 12) = 561x^5 + 1529x^4 + 6122x^3 + 5535x^2 + 2994x + 612
((17x^3 + 35x^2 + 61x + 14) * (33x^2 + 22x + 12)) + ((95x + 37) * (33x^2 + 22x + 12)) = 561x^5 + 1529x^4 + 6122x^3 + 5535x^2 + 2994x + 612
((17x^3 + 35x^2 + 61x + 14) - (95x + 37)) * (33x^2 + 22x + 12) = 561x^5 + 1529x^4 - 148x^3 - 1087x^2 - 914x - 276
((17x^3 + 35x^2 + 61x + 14) * (33x^2 + 22x + 12)) - ((95x + 37) * (33x^2 + 22x + 12)) = 561x^5 + 1529x^4 - 148x^3 - 1087x^2 - 914x - 276


TESTING: polynoms division...

(17x^3 + 35x^2 + 61x + 14) / (33x^2 + 22x + 12) = 0.51515152x + 0.71717172 :: 39.040404x + 5.3939394
((0.51515152x + 0.71717172) * (33x^2 + 22x + 12)) + (39.040404x + 5.3939394) = 17.x^3 + 35.x^2 + 61.x + 14.

(17x^3 + 35x^2 + 61x + 14) / (95x + 37) = 0.17894737x^2 + 0.29872576x + 0.52575944 :: -5.4530993
((0.17894737x^2 + 0.29872576x + 0.52575944) * (95x + 37)) + (-5.4530993) = 17.x^3 + 35.x^2 + 61.x + 14.

(33x^2 + 22x + 12) / (95x + 37) = 0.34736842x + 9.6288089e-002 :: 8.4373407
((0.34736842x + 9.6288089e-002) * (95x + 37)) + (8.4373407) = 33.x^2 + 22.x + 12.

((95x + 37) * (33x^2 + 22x + 12)) / (95x + 37) = 33.x^2 + 22.x + 12. :: 0

((33x^2 + 22x + 12) * (95x + 37)) / (33x^2 + 22x + 12) = 95.x + 37. :: 0

((33x^2 + 22x + 12) * (17x^3 + 35x^2 + 61x + 14)) / (33x^2 + 22x + 12) = 17.x^3 + 35.x^2 + 61.x + 14. :: 0

((17x^3 + 35x^2 + 61x + 14) * (33x^2 + 22x + 12)) / (17x^3 + 35x^2 + 61x + 14) = 33.x^2 + 22.x + 12. :: 0

((95x + 37) * (17x^3 + 35x^2 + 61x + 14)) / (95x + 37) = 17.x^3 + 35.x^2 + 61.x + 14. :: 0

((17x^3 + 35x^2 + 61x + 14) * (95x + 37)) / (17x^3 + 35x^2 + 61x + 14) = 95.x + 37. :: 0


TESTING: binomial polynoms...

binom (1) = x + 1
[1] = 2
binom (2) = x^2 + 2x + 1
[1] = 4
binom (3) = x^3 + 3x^2 + 3x + 1
[1] = 8
binom (4) = x^4 + 4x^3 + 6x^2 + 4x + 1
[1] = 16
binom (5) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1
[1] = 32
binom (6) = x^6 + 6x^5 + 15x^4 + 20x^3 + 15x^2 + 6x + 1
[1] = 64
binom (7) = x^7 + 7x^6 + 21x^5 + 35x^4 + 35x^3 + 21x^2 + 7x + 1
[1] = 128
binom (8) = x^8 + 8x^7 + 28x^6 + 56x^5 + 70x^4 + 56x^3 + 28x^2 + 8x + 1
[1] = 256
binom (9) = x^9 + 9x^8 + 36x^7 + 84x^6 + 126x^5 + 126x^4 + 84x^3 + 36x^2 + 9x + 1
[1] = 512

TESTING: combine polynoms...

(33x^2 + 22x + 12) <*> (17x^3 + 35x^2 + 61x + 14) = 9537x^6 + 39270x^5 + 108867x^4 + 156992x^3 + 155903x^2 + 57706x + 6788

(17x^3 + 35x^2 + 61x + 14) <*> (33x^2 + 22x + 12) = 610929x^6 + 1221858x^5 + 1519155x^4 + 1120460x^3 + 585233x^2 + 181390x + 35162

(95x + 37) <*> (33x^2 + 22x + 12) = 3135x^2 + 2090x + 1177

(33x^2 + 22x + 12) <*> (95x + 37) = 297825x^2 + 234080x + 46003

(95x + 37) <*> (17x^3 + 35x^2 + 61x + 14) = 1615x^3 + 3325x^2 + 5795x + 1367

(17x^3 + 35x^2 + 61x + 14) <*> (95x + 37) = 14575375x^3 + 17346050x^2 + 6884650x + 911287


} <poly_test.awl> #237 / [82]