1 | initial version |

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()`

.

2 | No.2 Revision |

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
```

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