DERIVE for Windows version 5.02 DfW file saved on 15 Aug 2003 9Aux(a, b):=PROG(IF(a < b, [0, a]), q := (MP2(a, b))1, r := (MP2(a, b))2, LOOP(RETURN [q, r])) Aux2(a, b):=PROG(IF(a < b, [0, a]), q := (MP2(a, b))1, r := (MP2(a, b))2, LOOP(q := q + (MP2(r, b))1, a := r, RETURN [q, a])) BELL(n):=(ITERATE(APPEND([(v_(DIM(v_) - k_)COMB(DIM(v_) - 1, k_), k_, 0, DIM(v_) - 1)], v_), v_, [1], n))1 BERNOULLI(n):=IF(n = 0, 1, IF(n = 1, - 1/2, - n(1 - n))) BERNOULLI_POLY(n, x):=IF(n = 1, x - 1/2, nLIM((k^(n - 1), k, 1, x_ - 1), x_, x) + BERNOULLI(n)) CATALAN(n):=COMB(2n, n)/(n + 1) CENTERED(n, p):=CENTERED_PYRAMID(n, p, 2) CENTERED_CUBE(n, d):=n^d + (n - 1)^d CENTERED_HEX(n, d):=n^(d + 1) - (n - 1)^(d + 1) CENTERED_PYRAMID(n, p, d):=COMB(n + d + -3, d - 2) + pCOMB(n + d + -2, d) CF(b, a, x, n):=ITERATES(b + a/r, r, x, n) DE2(a, b):=PROG(IF( INTEGER?(a) INTEGER?(b) a < 0 b 0, RETURN " Introdueix a i b naturals, b0 "), u := (TDEE(a, b))1, v := (TDEE(a, b))2, n := DIM(v), x := un, y := vn, LOOP(IF(y = a n = 1, RETURN [" Quocient =", x; " Residu =", a - y]), IF(y < a, PROG(y := y + v(n - 1), x := x + u(n - 1)), PROG(y := y - vn + v(n - 1), x := x - un + u(n - 1))), n := n - 1)) DEE(a, b):=PROG(IF( INTEGER?(a) INTEGER?(b) a < 0 b 0, RETURN " Introdueix a i b naturals, b0 "), u := (TDEE(a, b))1, v := (TDEE(a, b))2, n := DIM(v), x := un, y := vn, LOOP(IF(y = a n = 1, RETURN [" Quocient =", x; " Residu =", a - y]), IF(y < a, PROG(y := y + v(n - 1), x := x + u(n - 1)), PROG(y := v(n - 1) - vn + y, x := u(n - 1) - un + x)), n := n - 1)) DEE2(a, b):=PROG(d := (TDEE(a, b))1, w := (TDEE(a, b))2, n := DIM(w), c := [], v := [wn], LOOP(IF((v) = a s := 1, RETURN [" Quocient =", (c); " Residu =", a - (v)]), n := n - 1, IF((v) < a, PROG(v := APPEND(v, [wn]), c := APPEND(c, [d(n + 1)]))), p := DIM(v), v := APPEND(DELETE(v, p), [wn]), RETURN [c, p, v])) DEE33(a, b):=PROG(u := (TDEE(a, b))1, v := (TDEE(a, b))2, n := DIM(v), s := n) DEEG(a, b):=PROG(u := (TDEE(a, b))1, v := (TDEE(a, b))2, n := DIM(v), x := [un], y := [vn], LOOP(IF((y) = a n = 1, RETURN [" Quocient =", (x); " Residu =", a - (y)]), n := n - 1, IF((y) < a, PROG(y := APPEND(y, [vn]), x := APPEND(x, [un])), PROG(p := DIM(y), q := DIM(x), y := APPEND(DELETE(y, p), [vn]), x := APPEND(DELETE(x, q), [un]))))) DEEg(a, b):=PROG(u := (TDEE(a, b))1, v := (TDEE(a, b))2, n := DIM(v), s := n, x := [], y := [vn], LOOP(IF((y) = a s := 1, RETURN [" Quocient =", (x); " Residu =", a - (y)]), s := s - 1, IF((y) < a, PROG(y := APPEND(y, [vs]), x := APPEND(x, [u(s + 1)])), PROG(p := DIM(y), y := APPEND(DELETE(y, p), [v(s - 1)]))))) DISTINCT_PARTS(n):=(IF(8n - 16i_ + 1 = FLOOR((8n - 16i_ + 1))^2, PARTS(i_), 0), i_, 0, n/2) DISTINCT_PARTS_AUX(n, m):=IF(n < 2m, 1, 1 + (DISTINCT_PARTS_AUX(n - k_, k_ + 1), k_, m, FLOOR(n, 2))) Divent2(a, b):=PROG(IF(a < b, [0, a]), q := (MP2(a, b))1, r := (MP2(a, b))2, LOOP(IF(r < b, RETURN [q, r]), q := q + (MP2(r, b))1, a := r)) Divent2x(a, b):=PROG(IF(a < b, ["quocient =", 0; " residu =", a]), q := (MP2(a, b))1, LOOP(r := (MP2(a, b))2, IF(r < b, RETURN ["quocient =", q; " residu =", r]), q := q + (MP2(r, b))1, a := r)) Divisio(a, b):=PROG(n := 0, LOOP(IF(nb > a, RETURN ["quocient =", n - 1; " residu =", a - (n - 1)b]), n :+ 1)) Divisio2(a, b):=PROG(IF( INTEGER?(a) INTEGER?(b) a < 0 b 0, RETURN " Introdueix a i b naturals, b0 "), n := 1, LOOP(IF(nb > a, RETURN ["quocient =", n - 1; " residu =", a - (n - 1)b]), n :+ 1)) DivisioEntera2(a, b):=PROG(IF(a < b, ["quocient =", 0; " residu =", a]), q := (MP2(a, b))1, LOOP(r := (MP2(a, b))2, IF(r < b, RETURN ["quocient =", q; " residu =", r]), q := q + (MP2(r, b))1, a := r)) EULER(n):=IF(MOD(n, 2) = 1, 0, 2^nEULER_POLY(n, 1/2)) EULER_POLY(n, x):=2/(n + 1)(BERNOULLI_POLY(n + 1, x) - 2^(n + 1)BERNOULLI_POLY(n + 1, x/2)) HEX(n):=CENTERED(n, 6) MP2(a, b):=PROG(k := 1, w := [1, a - b], LOOP(IF(2kb > a, RETURN w), k :* 2, w := [k, a - kb])) OCTAHEDRAL(n):=CENTERED_PYRAMID(n, 4, 3) PARTS(n):=IF(n < 2, 1, FLOOR(APPROX((1/(k_/2)(IF(GCD(h_, k_) = 1, COS((((i_/k_ - 1/2)(MOD(i_h_/k_) - 1/2), i_, 1, k_ - 1) - 2nh_/k_)), 0), h_, 1, k_)(- 26^(- (24n - 1)/(6k_))(^((24n - 1)/(3k_))(6k_ - (24n - 1)) - 6k_ + - (24n - 1))/(k_(24n - 1)^(3/2))), k_, 1, n/LOG(n, 11)), LOG(1/(4n3)^((2n/3)), 10) + 5) + 1/2)) PARTS_AUX(n, m):=IF(n < 2m, 1, 1 + (PARTS_AUX(n - k_, k_), k_, m, FLOOR(n, 2))) PARTS_LIST(n):=REVERSE((ITERATE(IF(n < DIM(p_), [p_, v_, m_], [APPEND([p_v_], p_), APPEND(v_, [IF((3m_^2 - m_)/2 = DIM(p_) + 1 (3m_^2 + m_)/2 = DIM(p_) + 1, (-1)^(m_ + 1), 0)]), IF((3m_^2 + m_)/2 = DIM(p_) + 1, m_ + 1, m_)]), [p_, v_, m_], [[1], [1], 1], n))1) PENTATOPE(n):=POLYGONAL_PYRAMID(n, 3, 4) POLYGONAL(n, p):=POLYGONAL_PYRAMID(n, p, 2) POLYGONAL_PYRAMID(n, p, d):=COMB(n + d + -2, d - 1)(n(p - 2) - p + d + 2)/d RECURRENCE(u, v, v0, m):=REVERSE(ITERATE(APPEND([u], v), v, v0, m - DIM(v0))) RHOMBIC_DODECAHEDRAL(n):=CENTERED_HEX(n, 3) STAR(n):=CENTERED(n, 12) STIRLING1(n, k):=IF(n < k, 0, IF(n = k, 1, (-1)^(n + k)((-1)^j_COMB(n - 1 + j_, n - k + j_)COMB(2n - k, n - k + -j_)STIRLING2(n - k + j_, j_), j_, 1, n - k, 1))) STIRLING2(n, k):=1/k!(COMB(k, j_)(-1)^(k - j_)j_^n, j_, 1, k, 1) STIRLING_CYCLE(n, k):=STIRLING1(n, k) STIRLING_SUBSET(n, k):=STIRLING2(n, k) TDEE(a, b):=PROG(k := 1, d := [0], w := [0], LOOP(IF(kb > a, RETURN [d, w]), w := APPEND(w, [kb]), d := APPEND(d, [k]), k :* 2)) TETRAHEDRAL(n):=POLYGONAL_PYRAMID(n, 3, 3) TRIANGULAR(n):=POLYGONAL(n, 3) f(x):=PROG(u := 1, LOOP(IF(ux > 10, RETURN ux), u := u + 1)) g(x):=(f(t), t, 1, x) h(x):=('f(t), t, 1, x) tdee(a, b):=PROG(k := 1, d := [0], w := [0], LOOP(IF(kb > a, [d, w]), w := APPEND(w, kb), d := APPEND(d, k), k :* 2)) a:=[1, 3, 4] n:=1 p:=182 u:=[0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 274877906944, 549755813888, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664, 140737488355328, 281474976710656, 562949953421312, 1125899906842624, 2251799813685248, 4503599627370496, 9007199254740992, 18014398509481984, 36028797018963968, 72057594037927936, 144115188075855872, 288230376151711744, 576460752303423488, 1152921504606846976, 2305843009213693952, 4611686018427387904, 9223372036854775808, 18446744073709551616, 36893488147419103232, 73786976294838206464, 147573952589676412928, 295147905179352825856, 590295810358705651712, 1180591620717411303424, 2361183241434822606848, 4722366482869645213696, 9444732965739290427392, 18889465931478580854784, 37778931862957161709568, 75557863725914323419136, 151115727451828646838272, 302231454903657293676544, 604462909807314587353088, 1208925819614629174706176, 2417851639229258349412352, 4835703278458516698824704, 9671406556917033397649408, 19342813113834066795298816, 38685626227668133590597632, 77371252455336267181195264, 154742504910672534362390528, 309485009821345068724781056, 618970019642690137449562112, 1237940039285380274899124224, 2475880078570760549798248448, 4951760157141521099596496896, 9903520314283042199192993792, 19807040628566084398385987584, 39614081257132168796771975168, 79228162514264337593543950336, 158456325028528675187087900672, 316912650057057350374175801344, 633825300114114700748351602688, 1267650600228229401496703205376, 2535301200456458802993406410752, 5070602400912917605986812821504, 10141204801825835211973625643008, 20282409603651670423947251286016, 40564819207303340847894502572032] v:=[0, 7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672, 57344, 114688, 229376, 458752, 917504, 1835008, 3670016, 7340032, 14680064, 29360128, 58720256, 117440512, 234881024, 469762048, 939524096, 1879048192, 3758096384, 7516192768, 15032385536, 30064771072, 60129542144, 120259084288, 240518168576, 481036337152, 962072674304, 1924145348608, 3848290697216, 7696581394432, 15393162788864, 30786325577728, 61572651155456, 123145302310912, 246290604621824, 492581209243648, 985162418487296, 1970324836974592, 3940649673949184, 7881299347898368, 15762598695796736, 31525197391593472, 63050394783186944, 126100789566373888, 252201579132747776, 504403158265495552, 1008806316530991104, 2017612633061982208, 4035225266123964416, 8070450532247928832, 16140901064495857664, 32281802128991715328, 64563604257983430656, 129127208515966861312, 258254417031933722624, 516508834063867445248, 1033017668127734890496, 2066035336255469780992, 4132070672510939561984, 8264141345021879123968, 16528282690043758247936, 33056565380087516495872, 66113130760175032991744, 132226261520350065983488, 264452523040700131966976, 528905046081400263933952, 1057810092162800527867904, 2115620184325601055735808, 4231240368651202111471616, 8462480737302404222943232, 16924961474604808445886464, 33849922949209616891772928, 67699845898419233783545856, 135399691796838467567091712, 270799383593676935134183424, 541598767187353870268366848, 1083197534374707740536733696, 2166395068749415481073467392, 4332790137498830962146934784, 8665580274997661924293869568, 17331160549995323848587739136, 34662321099990647697175478272, 69324642199981295394350956544, 138649284399962590788701913088, 277298568799925181577403826176, 554597137599850363154807652352, 1109194275199700726309615304704, 2218388550399401452619230609408, 4436777100798802905238461218816, 8873554201597605810476922437632, 17747108403195211620953844875264, 35494216806390423241907689750528, 70988433612780846483815379501056, 141976867225561692967630759002112, 283953734451123385935261518004224] v0:= w:=[0, 7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672, 57344, 114688, 229376, 458752, 917504, 1835008, 3670016, 7340032, 14680064, 29360128, 58720256, 117440512, 234881024, 469762048, 939524096, 1879048192, 3758096384, 7516192768, 15032385536, 30064771072, 60129542144, 120259084288, 240518168576, 481036337152, 962072674304, 1924145348608, 3848290697216, 7696581394432, 15393162788864, 30786325577728, 61572651155456, 123145302310912, 246290604621824, 492581209243648, 985162418487296, 1970324836974592, 3940649673949184, 7881299347898368, 15762598695796736, 31525197391593472, 63050394783186944, 126100789566373888, 252201579132747776, 504403158265495552, 1008806316530991104, 2017612633061982208, 4035225266123964416, 8070450532247928832, 16140901064495857664, 32281802128991715328, 64563604257983430656, 129127208515966861312, 258254417031933722624, 516508834063867445248, 1033017668127734890496, 2066035336255469780992, 4132070672510939561984, 8264141345021879123968, 16528282690043758247936, 33056565380087516495872, 66113130760175032991744, 132226261520350065983488, 264452523040700131966976, 528905046081400263933952, 1057810092162800527867904, 2115620184325601055735808, 4231240368651202111471616, 8462480737302404222943232, 16924961474604808445886464, 33849922949209616891772928, 67699845898419233783545856, 135399691796838467567091712, 270799383593676935134183424, 541598767187353870268366848, 1083197534374707740536733696, 2166395068749415481073467392, 4332790137498830962146934784, 8665580274997661924293869568, 17331160549995323848587739136, 34662321099990647697175478272, 69324642199981295394350956544, 138649284399962590788701913088, 277298568799925181577403826176, 554597137599850363154807652352, 1109194275199700726309615304704, 2218388550399401452619230609408, 4436777100798802905238461218816, 8873554201597605810476922437632, 17747108403195211620953844875264, 35494216806390423241907689750528, 70988433612780846483815379501056, 141976867225561692967630759002112, 283953734451123385935261518004224] x:=66363972998157290039502871190933 CTextObj {\rtf1\ansi\ansicpg1252\deff0\deflang3082{\fonttbl{\f0\fmodern\fprq1\fcharset2 DfW5 Printer;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs24 Podeu trobar el problema i les funcions, comentades en el fitxer \par } *<{\rtf1\ansi\ansicpg1252\deff0\deflang3082{\fonttbl{\f0\fmodern\fprq1\fcharset2 DfW5 Printer;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\b\f0\fs24 DivisioEgipcia3.pdf \par } CExpnObj8HNuevajTDEE(a,b):=PROG(k:=1,d:=[0],w:=[0],LOOP(IF(k*b>a,RETURN([d,w])),w:=APPEND(w,[k*b]),d:=APPEND(d,[k]),k:*2))8Nueva TDEE(149,7) Simp(Nueva5)y&1?#[[0,1,2,4,8,16],[0,7,14,28,56,112]]8 ,Nueva5"-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-"88(NuevavDEE(a,b):=PROG(IF(NOT(INTEGER?(a)) OR NOT(INTEGER?(b)) OR a<0 OR b<=0,RETURN(" Introdueix a i b naturals, b0 ")),u:=(TDEE(a,b)) SUB 1,v:=(TDEE(a,b)) SUB 2,n:=DIMENSION(v),x:=u SUB n,y:=v SUB n,LOOP(IF(y=a OR n=1,RETURN([[" Quocient =",x],[" Residu =",a-y]])),IF(y