e01d0b68-1aab-4895-88af-2a5960fcbcc3 148 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Funktionstest für das Maxima-Plugin

Test Suite for the Maxima Plugin

Maxima

t.0 0 time :

Die Musterergebnisse sind rechts neben dem Rand als Screenshots zu finden.

You find the reference results (screenshots) outside the right margin.

restart MaximaControl Restart complete.

$$ build_info args Maxima 5.33.0 2014-04-04 08:28:01 i686-pc-mingw32 GNU Common Lisp (GCL) GCL 2.6.10 51 sys

Voreinstellung und Umschaltung der internen Funktionen

Preset and switch for internal functions

Maxima kann die Funktionen int(), diff(), lim(), det() und sum() übernehmen.

Maxima can directly handle the functions int(), diff(), lim(), det() and sum()

Voreinstellung ist: keine Funktion übernehmen.

Current default is to let SMath handle all functions.

x 2^x / x ∞ lim x x ∞ lim

x sech x diff x sech x diff

x sin x int x sin x int

j j 1 n sum #

a 12 b 322 mat * det a 12 b 322 mat * det

takeover MaximaControl int(), diff(), lim() and det() now use Maxima

Übernahme aller Funktionen außer sum()

Takeover of all functions except sum()

x sech x diff x sech x tanh * -

x 2^x / x ∞ lim ∞

j j 1 n sum #

x sin x int x cos -

a 12 b 322 mat * det a 2^32 b * - (*

sum() MaximaTakeover sum() now use Maxima

Jetzt sollte nur sum() durch Maxima erledigt werden.

Just sum() is handled by Maxima

x sech x diff x sech x diff

x 2^x / x ∞ lim x x ∞ lim

j j 1 n sum n 1 n + (* 2 /

x sin x int x sin x int

a 12 b 322 mat * det a 12 b 322 mat * det

det() int() MaximaTakeover det() and int() now use Maxima

Jetzt sollte nur det() durch Maxima erledigt werden.

x sech x diff x sech x diff

x 2^x / x ∞ lim x x ∞ lim

j j 1 n sum #

x sin x int x cos -

a 12 b 322 mat * det a 2^32 b * - (*

none MaximaTakeover All functions now are native SMath.

x 2^x / x ∞ lim x x ∞ lim

x sech x diff x sech x diff

x sin x int x sin x int

j j 1 n sum #

a 12 b 322 mat * det a 12 b 322 mat * det

all MaximaTakeover int(), diff(), det(), lim() and sum() now use Maxima

x sech x diff x sech x tanh * -

x sin x int x cos -

x 2^x / x ∞ lim ∞

j j 1 n sum n 1 n + (* 2 /

a 12 b 322 mat * det a 2^32 b * - (*

surrender MaximaControl All functions now are native SMath.

x sech x diff x sech x diff

x 2^x / x ∞ lim x x ∞ lim

j j 1 n sum #

x sin x int x sin x int

a 12 b 322 mat * det a 12 b 322 mat * det

takeover MaximaControl int(), diff(), lim() and det() now use Maxima

Umgang mit Maßeinheiten

Unit handling

10 N m / * x 02 m * int 20 N *

2 m * 3 km * + Maxima 3002 m *

a 3 m * + 500 cm * ≡ a Solve a 2 m * ≡

Griechische Buchstaben

Greek Characters

ΑΓΔΘΛΞ.ΠΣΦΨΩ Maxima ΑΓΔΘΛΞ.ΠΣΦΨΩ

αβγδεζηθικ.λμνξοπρστυφχψω Maxima αβγδεζηθικ.λμνξοπρστυφχψω

Zeichenketten

Strings

a b\\c abc 21 sys Maxima a b\\c abc 21 sys

äöüß° Maxima äöüß°

a+b Maxima a+b

a $b_c$ + d + Maxima d b.c + a +

$[x,y]$ Maxima x y 21 sys

$[[x=1,y=2],[x=2,y=3]]$ Maxima x 1 ≡ (y 2 ≡ (21 sys x 2 ≡ (y 3 ≡ (21 sys 21 sys

$2.1e100$ Maxima 2.1 10100 +^*

$2.1b100$ Maxima 2.1 10100^*

Weitere Übersetzungstests

Further translation tests

Spezielle Konstanten

Special constants

2 π * Maxima 2 π *

i sin Maxima i 1 sinh *

e i^e i^* Maxima e 2 i *^

2.3 π * (Maxima 23 π * 10 /

Dezimaltrennzeichen

Decimal delimiter

Argumenttrennzeichen

Argument delimiter

a b dummy Maxima a b dummy

Matrizen

Matrices

12 x.y a 22 mat Maxima 12 x.y a 22 mat

12 x.y a 22 mat Maxima 12 x.y a 22 mat

Vektorindizes

Vector indices

v k el Maxima v k el

Matrixindizes

Matrix indizes

M j k el Maxima M j k el

Logische Operatoren

Boolean and relational operators

a b ≤ Maxima a b ≤

a b ≥ Maxima a b ≥

a b ≠ Maxima a b ≠

a b & Maxima a b &

a b | Maxima a b |

matrices of lists

x 1 ≡ y 2 ≡ 21 sys x 2 ≡ y 3 ≡ 21 sys 12 mat Maxima x 1 ≡ (y 2 ≡ (21 sys x 2 ≡ (y 3 ≡ (21 sys 12 mat

a b 21 sys c d 21 sys f 11 sys Maxima a b 21 sys c d 21 sys f 11 sys

Lists and functions with multiple arguments

x y f a 21 sys 2 x.y a 22 mat Maxima x y f a 21 sys 2 x.y a 22 mat

Matrices, lists and functions with multiple arguments

Übersetzungen SMath->Maxima

Single sided translation SMath->Maxima

x y log string Maxima log(x)/log(y)

x y log

a b 21 sys string Maxima [a,b]

Listen

Lists

Funktion ODE.2 und Abfangen von Vorzeichenfragen

Function ODE.2 and handling of Maxima asking questions about signs

t w t 2 diff ω 2^t w * + 0 ≡ (t w t ODE.2 ω is assumed to be positive. t w k1 e i ω * t * (^* k2 e i ω * t * (-^* + ≡ 21 sys

ω 0 > assume Maxima ω 0 > (11 sys

t w t 2 diff ω 2^t w * + 0 ≡ (t w t ODE.2 Assign k1 ω t * sin * k2 ω t * cos * +

Funktionen Solve(), Algsys(), LinSolve() und Assign()

Functions Solve(), Algsys(), LinSolve() and Assign()

x 2^3 x * y * + y 2^+ 0 ≡ 3 x * y + 1 ≡ 21 mat x y 21 mat Solve 1 el Assign 3 - 5 sqrt + 2 / - 7 - 35 sqrt * + 2 / 21 sys

x y Clear 1

eq.1 x 2^3 x * y * + y 2^+ 0 ≡ (:

eq.2 3 x * y + 1 ≡ (:

eq.1 eq.2 21 mat x y 21 mat Algsys x 3 - 5 sqrt + 2 / - (≡ (y 7 - 35 sqrt * + 2 / ≡ (21 sys x 35 sqrt + 2 / ≡ (y 735 sqrt * + 2 / - (≡ (21 sys 12 mat

eq 2 el 2 a * x * y - 2 a 2^* ≡ (:

eq 1 el x z + y ≡ (:

eq 3 el y 2 z * - 2 ≡ (:

eq Unknowns a x y z 41 mat

eq x y z 31 sys LinSolve x 1 a + (≡ (y 2 a * ≡ (z 1 - a + (≡ (31 sys

Vorzeichenannahmen für Maßeinheiten

Units are assumed to be positive

x.0 10 mm * :

y.0 50 mm * :

ε.0 0.05 :

x y y.0 x x.0 / (2^* :

x ε ε.0 x x.0 / (* :

x ε 1 x y x diff (2^+ sqrt * x 0 x.0 int mm 1.6901

Kreuzprodukt mit skalierten Vektoren

Cross product with scaled vectors

a a.1 a.2 a.3 31 mat :

b b.1 b.2 b.3 31 mat :

c c.1 c.2 c.3 31 mat :

λ a * (b † Maxima λ a.2 b.3 * a.3 b.2 * - (* λ a.3 b.1 * a.1 b.3 * - (* λ a.1 b.2 * a.2 b.1 * - (* 31 mat

λ a * (b † #

a b c † (* a.1 b.2 c.3 * b.3 c.2 * - (* a.2 b.3 c.1 * b.1 c.3 * - (* + a.3 b.1 c.2 * b.2 c.1 * - (* +

λ a * (b c † (* λ a.1 b.2 c.3 * b.3 c.2 * - (* a.2 b.3 c.1 * b.1 c.3 * - (* + a.3 b.1 c.2 * b.2 c.1 * - (* + (*

a λ b * (c † (* #

a b λ * (* c † Maxima λ b.2 c.3 * b.3 c.2 * - (a.1 * b.3 c.1 * b.1 c.3 * - (a.2 * + b.1 c.2 * b.2 c.1 * - (a.3 * + (*

a b c Clear 1

Warnungen und Zusatzinformationen abfangen

Handling of warnings and messages

x cos 12 sqrt / ≡ x Solve solve: using arc-trig functions to get a solution.
Some solutions will be lost. x π 4 / ≡ (21 sys

x 1 - abs x / x 1 - 1 int Principal Value 2 - 21 sys

L 2 s a - (* s a + (* s 3^b s 2^* a 1 a b * - (* + (* / s t ilt Maxima :

L a*b*(a*b-1) is assumed to be positive. 21 - a b * + (* 1 a b * 1 - a b * + (* sqrt t * b / cosh - (* a 2^t 2^* 1 a b * 2 - a b * + (* + (* + a 1 a b * 2 - a b * + (* + (* 1 - a b * + (* / 21 sys

Rückübersetzung von at()

Back-translation of at()

t delta t 2 diff t s laplace Maxima t delta t diff t 0 ≡ at - s 2^+ 0 delta s * -

Plotting with plot2d

dir DocumentDirectory CurrentDirectory :

ans gnuplot.term png small size 250,250 21 sys set.plot_option Maxima :

ans gnuplot.preamble set key bottom right; set grid 21 sys set.plot_option Maxima :

plot x asin x acos x asinh x atanh 41 sys x π - π 31 sys gnuplot.out_file Test_plot2d.png 21 sys plot2d Maxima :

plot plot2d: expression evaluates to non-numeric value somewhere in plotting range. plot2d: expression evaluates to non-numeric value somewhere in plotting range. plot2d: expression evaluates to non-numeric value somewhere in plotting range. C:/Users/Kraska/maxout.gnuplot
C:/Users/Kraska/Test_plot2d.png 41 sys

Test_plot2d.png

Draw2D() with special characters and automatic temporary filename

p title Grüne Kurve auf Weiß bei 20°C ≡ color green ≡ x sin x π - π explicit grid true ≡ 41 sys 30015021 sys Draw2D :

p title Grüne Kurve auf Weiß bei 20°C ≡ color green ≡ x sin x π - π explicit grid true ≡ 41 sys grün.png 30015021 sys Draw2D :

Result format of Eigenvalues and -vectors

1005050022 mat eigenvectors Maxima 5012 sqrt - (* 5012 sqrt + (* 1122 mat 112 sqrt + (- 12 mat 11 - 2 sqrt + 12 mat 21 mat 12 mat

1 m * 00030001 m * 33 mat eigenvectors Maxima m 32122 mat 10000123 mat 01013 mat 21 mat 12 mat

Translation of derivatives improved

diff() MaximaTakeover diff() now use Maxima

diff(3) is used only if exponent is greater than 1

x y f y diff x diff x y f y diff x diff

x y f x 2 diff x y f x 2 diff

x y z f z diff y diff x diff x y z f z diff y diff x diff

x y z^+ sin z diff y diff x diff y ln z * x y z^+ cos y z^* x y z^+ sin + (* y z 1 - z + (*^x y z^+ sin * + y 12 z * - z +^/ -

r φ f r φ g 21 sys r φ 21 sys jacobian Maxima r φ f r diff r φ f φ diff r φ g r diff r φ g φ diff 22 mat

Test of diff(1)

x f x g * (diff x f x g x diff * x g x f x diff * +

x sin x ln * (diff x sin x / x cos x ln * +

x g f (diff x g f x diff

x 2^sin (diff 2 x * x 2^cos *

Funktionsaufrufe

Function calls

a f a 2^:

b mm * f b 2^m 2^* 1000000 /

b mm * f Maxima m 2^b 2^* 1000000 /

b mm * (f Maxima m 2^b 2^* 1000000 /

Names with underscores and separators

a_b_c_d Maxima a.b.c.d

a_b_c_d string Maxima a_b_c_d

a.b.c.d Maxima a.b.c.d

a.b.c.d string Maxima a_b_c_d

a.b.c Maxima a.b.c

a.b.c string Maxima a_b_c

1.2 2.3 21 sys Maxima 1.2 2.3 21 sys

Loading of abs_integrate

restart MaximaControl Restart complete.

all MaximaTakeover int(), diff(), det(), lim() and sum() now use Maxima

x f x 3^6 x 2^* - 8 x * + :

x f abs x 03 int 234 /

Definition in SMath and Maxima

A 3 MaximaDefine 3

A 3

Evaluate in SMath

$A$ Maxima 3

Evaluate in Maxima (using string input)

Transfer of an existing SMath-Definition to Maxima

C 2321 sys :

D 4 :

Definition in SMath

C D MaximaDefine 2321 sys 421 sys

Transfer the definitions to Maxima

D C Clear 1

Clear the definition in SMath

D C * Maxima 81221 sys

Still available in Maxima

D C kill Maxima done

Clear the definitions in Maxima

D C * Maxima C D *

Sum handling

sum() MaximaTakeover sum() now use Maxima

v 12331 mat :

v j el j 1 v rows sum apply: subscript must be an integer; found: ?g36311
#0: el(x=matrix([1],[2],[3]),y=[?g36311])
 -- an error. To debug this try: debugmode(true);
(%i35)

0 time t.0 - 31.777 s *