If I correctly understand your question, you want to plot some *symbolic* function such as $x\mapsto A \sin(wx)$, where $A$ and $w$ are symbolic variables. This is not *per se* possible since plotting needs floating point values. The solution consists in plotting $x\mapsto \sin(x)$ and changing the labels on the axes. The command

```
plot(sin(x), (x,-2*pi, 2*pi), ticks = [xt, yt], tick_formatter = [xt_lbl, yt_lbl])
```

plots the function $x\mapsto \sin(x)$, putting *ticks* on the x-axis at each location given in the list `xt`

, and *ticks* on the y-axis using `yt`

. The lists `xt_lbl`

and `yt_lbl`

are the labels at each tick. For instance,

```
sage: xt = [k * pi for k in range(-2,3)]
sage: xt_lbl = ['$-2\pi/w$', '$-\pi/w$', '$0$', '$\pi/w$', '$2\pi/w$']
sage: yt = [k / 2 for k in range(-2, 3)]
sage: yt_lbl = ['$-A$', '$-A/2$', '$0$', '$A/2$', '$A$']
sage: plot(sin(x),(x,-2*pi,2*pi), ticks=[xt, yt], tick_formatter = [xt_lbl, yt_lbl])
Launched png viewer for Graphics object consisting of 1 graphics primitive
```

creates the following plot:

For more information on `ticks`

and `tick_formatter`

, please refer to the documentation on 2D-plotting (search for "ticks" in the page) and the options of `show()`

.

**Addendum.** You may want to automatize the process a bit more. If you accept to personalize a bit less the labels, this is possible: you can use SageMath's capabilities in the simplification of symbolic expressions, combined with the function `latex`

which produces a LaTeX output from an expression. The following example should be self-explanatory.

```
sage: xt = [k * pi for k in range(-2, 3)]
sage: yt = [k/2 for k in range(-2, 3)]
sage: var('w,A')
(w, A)
sage: xt_lbl = ['$' + latex(t/w) + '$' for t in xt]
sage: yt_lbl = ['$' + latex(A*t) + '$' for t in yt]
sage: plot(sin(x),(x,-2*pi, 2*pi), ticks=[xt, yt], tick_formatter=[xt_lbl, yt_lbl])
Launched png viewer for Graphics object consisting of 1 graphics primitive
```

Please give the mathematical description of the task. (To plot something, one needs to evaluate to a real number a function, so there should be no variables as obstacles for the plot around.)

So we

first fixparameters $w,A$, and need a 2D-plot of the function of one variable, $x$, given by the formula $$ f(x) = A\sin(wx)\ ,$$ or wefix(and give) a variable $A$, and need a $3D$-Plot of the function $$g(x,w)=A\sin(wx)\ ,$$ or something related...?!The "ticks" are only simple marks on the coordinate axes?

Hi Dan, thanks for your reply. The first option you gave was the situation I was trying to describe: Fix parameters

w,Aand get a 2D-plot of the function of variablex.And yes the tics I'm referring to are simple marks on the coordinate axes -I'm using gnuplot terminology there.

I know you could do this trivially with something like plot(y(x=x, w=2, A=5), (x,-pi(),pi())

But I was interested to see if Sage could plot it without me providing it a specific constant for

Aandw, but instead using the "assume" operator to define those constants as being real and positive, and plot with the axes expressed in terms ofAandwrather than numerically.Obviously this is just an example, the function I'm dealing with is a bit more complicated.

Does that clarify my question?