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Create a viable free open source alternative to Magma, Maple, Mathematica, and Matlab.
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933262154439441526816992388562667004907159682643816214685929638952175999\ 932299156089414639761565182862536979208272237582511852109168640000000000\ 00000000000000 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 |
1.7724538509055160272981674833411451827975494561223871282138077898529112\ 845910321813749506567385446654162268236242825706662361528657244226025250\ 937096027870684620376986531051228499251730289508262289320953792679628001\ 746390153514797205167001901852340185854469744949126403139217755259062164\ 054193325009063984076137334774751534336679897893658518364087954511651617\ 387600590673934317913328098548462481849020546548521956132515616474675150\ 427387610561079961271072100603720444836723652966137080943234988316684242\ 138457096091204204277857780686947665700052183056851254133966369446541815\ 107166938833219429293570622688652244205421499480499207564863988748385059\ 306402182140292858112330649789452036211490789622873894032459781985131348\ 712665125062932600446563821096750268124969305954204615607619522173915250\ 702077927580990543329006622230676144696612481887430699788352050614644438\ 541853079735742571791856359597499599522638492422038891039664064472939728\ 41345043002140564233433039261756134176336320017037654163476320669 1.772453850905516027298167483341145182797549456122387128213807789852911284591032181374950656738544665416226823624282570666236152865724422602525093709602787068462037698653105122849925173028950826228932095379267962800174639015351479720516700190185234018585446974494912640313921775525906216405419332500906398407613733477475153433667989789365851836408795451165161738760059067393431791332809854846248184902054654852195613251561647467515042738761056107996127107210060372044483672365296613708094323498831668424213845709609120420427785778068694766570005218305685125413396636944654181510716693883321942929357062268865224420542149948049920756486398874838505930640218214029285811233064978945203621149078962287389403245978198513134871266512506293260044656382109675026812496930595420461560761952217391525070207792758099054332900662223067614469661248188743069978835205061464443854185307973574257179185635959749959952263849242203889103966406447293972841345043002140564233433039261756134176336320017037654163476320669 |
3.1415926535897932384626433832795028841971693993751058209749445923078164\ 062862089986280348253421170679821480865132823066470938446095505822317253\ 594081284811174502841027019385211055596446229489549303819644288109756659\ 334461284756482337867831652712019091456485669234603486104543266482133936\ 072602491412737245870066063155881748815209209628292540917153643678925903\ 600113305305488204665213841469519415116094330572703657595919530921861173\ 819326117931051185480744623799627495673518857527248912279381830119491298\ 336733624406566430860213949463952247371907021798609437027705392171762931\ 767523846748184676694051320005681271452635608277857713427577896091736371\ 787214684409012249534301465495853710507922796892589235420199561121290219\ 608640344181598136297747713099605187072113499999983729780499510597317328\ 160963185950244594553469083026425223082533446850352619311881710100031378\ 387528865875332083814206171776691473035982534904287554687311595628638823\ 53787593751957781857780532171226806613001927876611195909216420199 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420199 |
3.1415926535897932384626433832795028841971693993751058209749445923078164\ 062862089986280348253421170679821480865132823066470938446095505822317253\ 594081284811174502841027019385211055596446229489549303819644288109756659\ 334461284756482337867831652712019091456485669234603486104543266482133936\ 072602491412737245870066063155881748815209209628292540917153643678925903\ 600113305305488204665213841469519415116094330572703657595919530921861173\ 819326117931051185480744623799627495673518857527248912279381830119491298\ 336733624406566430860213949463952247371907021798609437027705392171762931\ 767523846748184676694051320005681271452635608277857713427577896091736371\ 787214684409012249534301465495853710507922796892589235420199561121290219\ 608640344181598136297747713099605187072113499999983729780499510597317328\ 160963185950244594553469083026425223082533446850352619311881710100031378\ 387528865875332083814206171776691473035982534904287554687311595628638823\ 53787593751957781857780532171226806613001927876611195909216420199 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420199 |
2 * 3 * 7 * 19 2 * 3 * 7 * 19 |
x^5 - 1 x^5 - 1 |
(x^4 + x^3 + x^2 + x + 1)*(x - 1) (x^4 + x^3 + x^2 + x + 1)*(x - 1) |
(x^5 - 1)^3 (x^4 + x^3 + x^2 + x + 1)^3*(x - 1)^3 (x^5 - 1)^3 (x^4 + x^3 + x^2 + x + 1)^3*(x - 1)^3 |
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x/(x^2 - 1) x/(x^2 - 1) |
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1/2/(x + 1) + 1/2/(x - 1) 1/2/(x + 1) + 1/2/(x - 1) |
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\frac{1}{2 \, {\left(x + 1\right)}} + \frac{1}{2 \, {\left(x - 1\right)}} \frac{1}{2 \, {\left(x + 1\right)}} + \frac{1}{2 \, {\left(x - 1\right)}} |
[x == 2, x == -1] [x == 2, x == -1] |
[x == -3, x == -1, x == 2] [x == -3, x == -1, x == 2] |
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x - 1 == y + 1 x + 1 == 2*y - 2 x - 1 == y + 1 x + 1 == 2*y - 2 |
[[x == 7, y == 5]] [[x == 7, y == 5]] |
[{x: 7, y: 5}] [{x: 7, y: 5}] |
[[7.0, 5.0000]] [[7.0, 5.0000]] |
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(-0.32767, -0.4957550765359254871346963) (2.8077, 1.855755076535925487134696) (-0.32767, -0.4957550765359254871346963) (2.8077, 1.855755076535925487134696) |
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(1.000000000, 8.000000000, -4.883036880, -0.1396203900) (1.000000000, 8.000000000, 3.549703547, -1.193712943) (1.000000000, 8.000000000, -4.883036880, -0.1396203900) (1.000000000, 8.000000000, 3.549703547, -1.193712943) |
Try a random 3 by 3 matrix with integer entries. Then calculate its determinant.
<type 'sage.matrix.matrix_integer_dense.Matrix_integer_dense'> 39 Time: CPU 0.00 s, Wall: 0.00 s <type 'sage.matrix.matrix_integer_dense.Matrix_integer_dense'> 39 Time: CPU 0.00 s, Wall: 0.00 s |
Try a random 200 by 200 matrix with integer entries. Then time the calculation of its determinant. It could be a big number.
1 3 <type 'sage.matrix.matrix_integer_dense.Matrix_integer_dense'> -14382230777275826589566212167887142284022202947000473201750073971367920\ 653260467820935889968458550212479781015365015156203347597476573364560383\ 574201803886840423741839879833901820985502312201902589867086430411262481\ 120475209803413262175401159033540547216117117017782120211302785040379159\ 124538202527695693944994729888152435993127745476801520782655482046465499\ 178358461181604148574107498068001571168294012935483809321263021696306732\ 000731690393250585869217175998640 Time: CPU 0.54 s, Wall: 0.54 s 1 3 <type 'sage.matrix.matrix_integer_dense.Matrix_integer_dense'> -14382230777275826589566212167887142284022202947000473201750073971367920653260467820935889968458550212479781015365015156203347597476573364560383574201803886840423741839879833901820985502312201902589867086430411262481120475209803413262175401159033540547216117117017782120211302785040379159124538202527695693944994729888152435993127745476801520782655482046465499178358461181604148574107498068001571168294012935483809321263021696306732000731690393250585869217175998640 Time: CPU 0.54 s, Wall: 0.54 s |
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Sage does Calculus:
15*(x^5 - 1)^2*x^4 15*(x^5 - 1)^2*x^4 |
1/16*x^16 - 3/11*x^11 + 1/2*x^6 - x 1/16*x^16 - 3/11*x^11 + 1/2*x^6 - x |
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cos(4)*e^4*sin(4)^2 cos(4)*e^4*sin(4)^2 |
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(x, y, u, v) (x, y, u, v) |
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Sage can draw 3d plots:
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t t |
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<type 'sage.symbolic.expression.Expression'> <type 'sage.symbolic.expression.Expression'> |
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c + beta/alpha c*e^alpha + beta/alpha c*e + beta/alpha c*e^(2*alpha) + beta/alpha c + beta/alpha c*e^alpha + beta/alpha c*e + beta/alpha c*e^(2*alpha) + beta/alpha |
t |--> 20*e^(1/2*t) + 80 t |--> 20*e^(1/2*t) + 80 |
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(k2*cos(1/4*sqrt(31)*t) + k1*sin(1/4*sqrt(31)*t))*e^(-1/4*t) (k2*cos(1/4*sqrt(31)*t) + k1*sin(1/4*sqrt(31)*t))*e^(-1/4*t) |
t |--> 1/2*(2*cos(1/4*sqrt(31)*t) + sin(1/4*sqrt(31)*t))*e^(-1/4*t) t |--> 1/2*(2*cos(1/4*sqrt(31)*t) + sin(1/4*sqrt(31)*t))*e^(-1/4*t) |
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-(log(-P + r(t)) - log(r(t)))/(P*alpha) == c + t -(log(-P + r(t)) - log(r(t)))/(P*alpha) == c + t |
-(P - r(t))/r(t) == K*e^(-P*alpha*t) -(P - r(t))/r(t) == K*e^(-P*alpha*t) |
[r(t) == -P*e^(P*alpha*t)/(K - e^(P*alpha*t))] [r(t) == -P*e^(P*alpha*t)/(K - e^(P*alpha*t))] |
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Sage can do graph theory:
Flower Snark: Graph on 20 vertices Flower Snark: Graph on 20 vertices |
Flower Snark: Graph on 20 vertices Flower Snark: Graph on 20 vertices |
Sage contains many unique and deep algorithms:
Permutation Group with generators [(2,11)(3,12)(4,13)(5,8)(6,9)(7,10)(16,19)(17,18), (1,14)(2,4)(5,7)(8,10)(11,13), (0,3,6,9,12)(1,4,7,10,13)(2,5,8,11,14)(15,16,17,18,19)] Permutation Group with generators [(2,11)(3,12)(4,13)(5,8)(6,9)(7,10)(16,19)(17,18), (1,14)(2,4)(5,7)(8,10)(11,13), (0,3,6,9,12)(1,4,7,10,13)(2,5,8,11,14)(15,16,17,18,19)] |
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