The public-domain Linux environment encourages compatibility among conforming applications, such that they can work together to solve complex tasks. This approach is in marked contrast to many closed-form commercial operating systems (Windows, macOS) and applications. Even commercial programs (e.g., Mathematica) that conform to standard Linux practices can work in concert with other applications.

Within SciComp@UNC, TeXmacs has been configured to embed sessions of other applications:

Asymptote

A general purpose vector graphics language

Asymptote]

size(5cm); for (int n = 3; n <= 7; ++n) { draw(shift(2.2*n, 0) * polygon(n));}

Asymptote]

Figure 1. Figure generated using folded Asymptote code

Eukleides

An environment for generation of geometrical figures

Eukleides]

box -1, -1, 7, 3 A B C isosceles H = projection(C, line(A, B)) draw (A.B.C) C.H dashed H end label A 180: B 0: C 90: B, H, C right B, A, C double C, B, A double A.H B.H A.C double C.B double end

Eukleides]

Gnuplot

Gnuplot is graphics application

GNUplot]

plot sin(cos(x))+cos(sin(x))

GNUplot]

Lisp

;; Loading file /opt/TeXmacs/plugins/lisp/clisp/clisp-init.lisp …
;;  Loading file lisp/tmlib.lisp …
;;  Loaded file lisp/tmlib.lisp

;; Loaded file /opt/TeXmacs/plugins/lisp/clisp/clisp-init.lisp

CLisp>

(car '(a b c))

A

CLisp>

(cdr '(a b c))

(B C)

CLisp>

Mathematica

Mathematica

In[1]:=

N[Pi,1000]

$3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420199$

In[2]:=

100!

${\displaystyle 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}$

In[4]:=

D[Sin[Cos[x]]+Cos[Sin[x]],{x,10}]

${\displaystyle 945{\sin }^5\left(x\right)\sin (\sin \left(x\right))-2205{\sin }^3\left(x\right)\sin (\sin \left(x\right))+\sin \left(x\right)\sin (\sin \left(x\right))-945\cos (\cos \left(x\right)){\cos }^5\left(x\right)+2205\cos (\cos \left(x\right))\cos {}^3\left(x\right)-\cos (\cos \left(x\right))\cos \left(x\right)+{\cos }^{10}\left(x\right)(-\cos (\sin \left(x\right)))-120\cos {}^8\left(x\right)\cos (\sin \left(x\right))+45\sin \left(x\right)\sin (\sin \left(x\right)){\cos }^8\left(x\right)+630\sin {}^2\left(x\right){\cos }^6\left(x\right)\cos (\sin \left(x\right))-2352{\cos }^6\left(x\right)\cos (\sin \left(x\right))+2730\sin \left(x\right)\sin (\sin \left(x\right)){\cos }^6\left(x\right)-3150{\sin }^3\left(x\right)\sin (\sin \left(x\right))\cos {}^4\left(x\right)+15750{\sin }^2\left(x\right){\cos }^4\left(x\right)\cos (\sin \left(x\right))-4725{\sin }^2\left(x\right)\cos {}^4\left(x\right)\sin (\cos \left(x\right))-5440{\cos }^4\left(x\right)\cos (\sin \left(x\right))-3150{\cos }^4\left(x\right)\sin (\cos \left(x\right))+19530\sin \left(x\right)\sin (\sin \left(x\right)){\cos }^4\left(x\right)+3150{\sin }^4\left(x\right)\cos (\cos \left(x\right)){\cos }^3\left(x\right)+22050{\sin }^2\left(x\right)\cos (\cos \left(x\right))\cos {}^3\left(x\right)+630{\sin }^6\left(x\right){\cos }^2\left(x\right)\sin (\cos \left(x\right))-4725{\sin }^4\left(x\right)\cos {}^2\left(x\right)\cos (\sin \left(x\right))+15750{\sin }^4\left(x\right){\cos }^2\left(x\right)\sin (\cos \left(x\right))-22050{\sin }^3\left(x\right)\sin (\sin \left(x\right)){\cos }^2\left(x\right)+25515{\sin }^2\left(x\right){\cos }^2\left(x\right)\cos (\sin \left(x\right))+25515{\sin }^2\left(x\right){\cos }^2\left(x\right)\sin (\cos \left(x\right))-256{\cos }^2\left(x\right)\cos (\sin \left(x\right))+255{\cos }^2\left(x\right)\sin (\cos \left(x\right))+7125\sin \left(x\right)\sin (\sin \left(x\right)){\cos }^2\left(x\right)-{\sin }^{10}\left(x\right)\sin (\cos \left(x\right))-45{\sin }^8\left(x\right)\cos (\cos \left(x\right))\cos \left(x\right)-120{\sin }^8\left(x\right)\sin (\cos \left(x\right))-2730{\sin }^6\left(x\right)\cos (\cos \left(x\right))\cos \left(x\right)-2352{\sin }^6\left(x\right)\sin (\cos \left(x\right))-19530{\sin }^4\left(x\right)\cos (\cos \left(x\right))\cos \left(x\right)-3150{\sin }^4\left(x\right)\cos (\sin \left(x\right))-5440{\sin }^4\left(x\right)\sin (\cos \left(x\right))-7125{\sin }^2\left(x\right)\cos (\cos \left(x\right))\cos \left(x\right)+255{\sin }^2\left(x\right)\cos (\sin \left(x\right))-256{\sin }^2\left(x\right)\sin (\cos \left(x\right))}$

In[5]:=

1 == 2

${\displaystyle \text{False}}$

In[6]:=

1 == 1

${\displaystyle \text{True}}$

In[7]:=

Eq = x==1

${\displaystyle x=1}$

In[8]:=

Eq /. x->1

${\displaystyle \text{True}}$

In[9]:=

ODE = y'[x] + x y[x] == Sin[x]

${\displaystyle y^{\text{'}}\left(x\right)+xy\left(x\right)=\sin \left(x\right)}$

In[14]:=

sol = DSolve[ODE,y[x],x]

${\displaystyle \left\{\{y\left(x\right)\to c_1{e}^{-\frac{x^2}{2}}-\frac{1}{2}i\sqrt{\frac{\pi }{2}}{e}^{\frac{1}{2}-\frac{x^2}{2}}(\text{erfi}\left(\frac{x+i}{\sqrt{2}}\right)-\text{erfi}(\frac{}{x-i}\sqrt{2}))\}\right\}}$

In[17]:=

z[x_] = y[x] /. sol[[1,1]]

${\displaystyle c_1{e}^{-\frac{x^2}{2}}-\frac{1}{2}i\sqrt{\frac{\pi }{2}}{e}^{\frac{1}{2}-\frac{x^2}{2}}(\text{erfi}\left(\frac{x+i}{\sqrt{2}}\right)-\text{erfi}(\frac{}{x-i}\sqrt{2}))}$

In[15]:=

sol[[1,1]]

${\displaystyle y\left(x\right)\to c_1{e}^{-\frac{x^2}{2}}-\frac{1}{2}i\sqrt{\frac{\pi }{2}}{e}^{\frac{1}{2}-\frac{x^2}{2}}(\text{erfi}\left(\frac{x+i}{\sqrt{2}}\right)-\text{erfi}(\frac{}{x-i}\sqrt{2}))}$

In[18]:=

z[1.]

${\displaystyle 0.606531c_1+(1.21479+0.i)}$

In[19]:=

Maxima

(%i1)

diff(sin(x),x);

${\displaystyle \text{(\%o1)}\cos \left(x\right)}$

(%i2)

Octave

${\displaystyle A={\displaystyle \left(\begin{array}{ccc}0.45229& 0.22986& 0.70938\\ 0.65207& 0.84622& 0.8479\\ 0.28058& 0.5938& 0.36148\end{array}\right)},A^{-1}={\displaystyle \left(\begin{array}{ccc}-11.373& 19.462& -23.333\\ 0.12663& -2.0461& 4.5509\\ 8.6198& -11.746& 13.402\end{array}\right)}}$

octave>

A=rand(3)

${\displaystyle \left(\begin{array}{ccc}0.93125& 0.050603& 0.82831\\ 0.22199& 0.11851& 0.75259\\ 0.09635& 0.24193& 0.66373\end{array}\right)}$

octave>

inv(A)

${\displaystyle \left(\begin{array}{ccc}1.5894& -2.5636& 0.9233\\ 1.15& -8.273& 7.9454\\ -0.6499& 3.3876& -1.5235\end{array}\right)}$

octave>

Python

Python]

from pylab import *

Python]

x=arange(0.,3.15,0.01); y=sin(x); plot(x,y);

Python]

show()

None

Python]

Shell

Shell session inside TeXmacs pid = 26400

Shell]

pwd

/home/student

Shell]

ls

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