# Question:How to obtain the extent of the x and y axis used in plot?

## Question:How to obtain the extent of the x and y axis used in plot?

Maple 2024

When making this plot, using smart plot (i.e. not giving the plot command the x=from..to and also not giving it y=from...to

`p:=plot(0,color=red);`

I need to programatically find the x=-10..10 and y=-1..1 from the variable p. But if I do

`rhs~(indets(p, identical("originalview")=anything));`

it gives

{[-10. .. 10., 0. .. 0.]}

But clearly looking at the plot the y axis is from -1..1

The reason I need to determine the view from the above plot, is that I need to use same view windows size in another plot not using smart plot (phase plot) which requires one to provide explicit x and y ranges. i.e I'd like the phase plot to have same view size in terms of x range and y range.

I printed the PLOT structure but do not see another field to look at.

Any idea or trick to find y=-1..1 values in this example ? I am using Maple 2024.1

```lprint(p)
PLOT(CURVES(Matrix(200,2,{(1, 1) = -10., (2, 1) = -9.89484789949749, (3, 1) =
-9.80335561909548, (4, 1) = -9.70046298090452, (5, 1) = -9.59688830351759, (6,
1) = -9.49380589849246, (7, 1) = -9.39823531356784, (8, 1) = -9.29927750854271,
(9, 1) = -9.19693520502513, (10, 1) = -9.09492111457286, (11, 1) =
-8.98998708341709, (12, 1) = -8.89756113165829, (13, 1) = -8.79351140100503, (
14, 1) = -8.6890344321608, (15, 1) = -8.58835151356784, (16, 1) =
-8.49692177788945, (17, 1) = -8.38820297889447, (18, 1) = -8.29610389547739, (
19, 1) = -8.18897076683417, (20, 1) = -8.09413979497487, (21, 1) =
-7.99009518894472, (22, 1) = -7.89102011959799, (23, 1) = -7.78764567839196, (
24, 1) = -7.69271567135678, (25, 1) = -7.59032083417085, (26, 1) =
-7.4839613758794, (27, 1) = -7.39137515477387, (28, 1) = -7.29137949949749, (29
, 1) = -7.18807420301508, (30, 1) = -7.08701012462312, (31, 1) =
-6.9892254321608, (32, 1) = -6.88065220301508, (33, 1) = -6.78309432763819, (34
, 1) = -6.67893047236181, (35, 1) = -6.58454253768844, (36, 1) =
-6.48135159396985, (37, 1) = -6.38425695778894, (38, 1) = -6.28276508643216, (
39, 1) = -6.18353823115578, (40, 1) = -6.07965690954774, (41, 1) =
-5.97960685025126, (42, 1) = -5.87729121407035, (43, 1) = -5.77582280301507, (
44, 1) = -5.68258387135678, (45, 1) = -5.57572153366834, (46, 1) =
-5.48014258492462, (47, 1) = -5.37823549045226, (48, 1) = -5.28069739798995, (
49, 1) = -5.17239388140703, (50, 1) = -5.07861099396985, (51, 1) =
-4.97216657788945, (52, 1) = -4.87515404824121, (53, 1) = -4.76903758693467, (
54, 1) = -4.67747702713568, (55, 1) = -4.57320023718593, (56, 1) =
-4.47247400603015, (57, 1) = -4.37181357688442, (58, 1) = -4.27152345929648, (
59, 1) = -4.17517605326633, (60, 1) = -4.07102195577889, (61, 1) =
-3.97175554874372, (62, 1) = -3.86728232964824, (63, 1) = -3.77270890854271, (
64, 1) = -3.66818757386935, (65, 1) = -3.56807434874372, (66, 1) =
-3.46820480201005, (67, 1) = -3.36389067336683, (68, 1) = -3.26781355276382, (
69, 1) = -3.16941743919598, (70, 1) = -3.06077643819095, (71, 1) =
-2.96241091055276, (72, 1) = -2.86181373366834, (73, 1) = -2.7595089959799, (74
, 1) = -2.66547103417085, (75, 1) = -2.5652296120603, (76, 1) =
-2.46575123417085, (77, 1) = -2.35934029145729, (78, 1) = -2.26543724422111, (
79, 1) = -2.15709262110553, (80, 1) = -2.05931995175879, (81, 1) =
-1.96257900603015, (82, 1) = -1.85855141105528, (83, 1) = -1.75410300301508, (
84, 1) = -1.65907041708543, (85, 1) = -1.5581500321608, (86, 1) = -1.4596616, (
87, 1) = -1.35289910050251, (88, 1) = -1.26051985527638, (89, 1) =
-1.15441893366834, (90, 1) = -1.05467848944724, (91, 1) = -.955901429145728, (
92, 1) = -.857045790954773, (93, 1) = -.756219297487437, (94, 1) =
-.649344903517589, (95, 1) = -.551351549748743, (96, 1) = -.454619526633167, (
97, 1) = -.351214585929648, (98, 1) = -.248034748743718, (99, 1) =
-.155424717587939, (100, 1) = -.0457214572864313, (101, 1) = .0460731437185924,
(102, 1) = .153437240201004, (103, 1) = .255905869346734, (104, 1) =
.347398149748743, (105, 1) = .4502907879397, (106, 1) = .553865465326634, (107,
1) = .656947870351759, (108, 1) = .752518455276382, (109, 1) = .851476260301508
, (110, 1) = .953818563819095, (111, 1) = 1.05583265427136, (112, 1) =
1.16076668542714, (113, 1) = 1.25319263718593, (114, 1) = 1.3572423678392, (115
, 1) = 1.46171933668342, (116, 1) = 1.56240225527638, (117, 1) =
1.65383199095477, (118, 1) = 1.76255078994975, (119, 1) = 1.85464987336683, (
120, 1) = 1.96178300201005, (121, 1) = 2.05661397386935, (122, 1) =
2.1606585798995, (123, 1) = 2.25973364924623, (124, 1) = 2.36310809045226, (125
, 1) = 2.45803809748744, (126, 1) = 2.56043293467337, (127, 1) =
2.66679239296482, (128, 1) = 2.75937861407035, (129, 1) = 2.85937426934673, (
130, 1) = 2.96267956582914, (131, 1) = 3.06374364422111, (132, 1) =
3.16152833668342, (133, 1) = 3.27010156582915, (134, 1) = 3.36765944120603, (
135, 1) = 3.47182329648241, (136, 1) = 3.56621123115578, (137, 1) =
3.66940217487437, (138, 1) = 3.76649681105528, (139, 1) = 3.86798868241206, (
140, 1) = 3.96721553768844, (141, 1) = 4.07109685929648, (142, 1) =
4.17114691859297, (143, 1) = 4.27346255477387, (144, 1) = 4.37493096582915, (
145, 1) = 4.46816989748744, (146, 1) = 4.57503223517588, (147, 1) =
4.6706111839196, (148, 1) = 4.77251827839196, (149, 1) = 4.87005637085427, (150
, 1) = 4.97835988743719, (151, 1) = 5.07214277487437, (152, 1) =
5.17858719095477, (153, 1) = 5.27559972060302, (154, 1) = 5.38171618190955, (
155, 1) = 5.47327674170854, (156, 1) = 5.57755353165829, (157, 1) =
5.67827976281407, (158, 1) = 5.7789401919598, (159, 1) = 5.87923030954774, (160
, 1) = 5.97557771557789, (161, 1) = 6.07973181306533, (162, 1) =
6.1789982201005, (163, 1) = 6.28347143919598, (164, 1) = 6.37804486030151, (165
, 1) = 6.48256619497488, (166, 1) = 6.5826794201005, (167, 1) =
6.68254896683417, (168, 1) = 6.78686309547739, (169, 1) = 6.8829402160804, (170
, 1) = 6.98133632964824, (171, 1) = 7.08997733065327, (172, 1) =
7.18834285829146, (173, 1) = 7.28894003517588, (174, 1) = 7.39124477286432, (
175, 1) = 7.48528273467337, (176, 1) = 7.58552415678392, (177, 1) =
7.68500253467337, (178, 1) = 7.79141347738694, (179, 1) = 7.88531652462311, (
180, 1) = 7.9936611477387, (181, 1) = 8.09143381708543, (182, 1) =
8.18817476281407, (183, 1) = 8.29220235778895, (184, 1) = 8.39665076582915, (
185, 1) = 8.49168335175879, (186, 1) = 8.59260373668342, (187, 1) =
8.69109216884422, (188, 1) = 8.79785466834171, (189, 1) = 8.89023391356784, (
190, 1) = 8.99633483517588, (191, 1) = 9.09607527939699, (192, 1) =
9.1948523396985, (193, 1) = 9.29370797788945, (194, 1) = 9.39453447135678, (195
, 1) = 9.50140886532663, (196, 1) = 9.59940221909548, (197, 1) =
9.69613424221106, (198, 1) = 9.79953918291458, (199, 1) = 9.9027190201005, (200
, 1) = 10.},datatype = float[8],storage = rectangular,order = Fortran_order,
shape = []),COLOUR(RGB,.47058824,0.,.54901961e-1,_ATTRIBUTE("source" =
"mathdefault"))),AXESLABELS("",""),VIEW(-10. .. 10.,DEFAULT,_ATTRIBUTE("source"
= "mathdefault")),_ATTRIBUTE("input" = [table([(1)=plot,(2)=[0]]),
"originalview" = [-10. .. 10., 0. .. 0.], "originalaxesticks" = AXESTICKS(
DEFAULT,DEFAULT,_ATTRIBUTE("source" = "mathdefault"))]))

```

Update

This below is a proc that takes PLOT data struct and returns correct x,y ranges.  It seems to work ok on few tests I did. Bug reports are welcome.

 > restart;
 > #gets a PLOT struct and returns correct x,y ranges get_x_y_range:=proc(p)::list; local T,from_x,to_x,from_y,to_y;    try       T:=plottools:-getdata(p,'rangesonly');    catch:       error StringTools:-FormatMessage( lastexception[2..-1] );    end try;   from_x := op(1,T[1]);   to_x   := op(2,T[1]);   from_y := op(1,T[2]);           to_y   := op(2,T[2]);                  if from_y=to_y then      if from_y<0 then         to_y   := 0;                         from_y := from_y-abs(from_y)/2;      elif from_y>0 then                              from_y := 0;         to_y   := to_y+to_y/2;     else         from_y := -1;         to_y   := 1;                     fi;                fi;   RETURN([from_x..to_x,from_y..to_y]);              end proc:
 > p := plot(6); get_x_y_range(p)

 > p := plot(-3); get_x_y_range(p)

 > p := plot(0); get_x_y_range(p)

 > p := plot(x); get_x_y_range(p)

 > p := plot(sin(x)); get_x_y_range(p)

 > p := plot(exp(x)); get_x_y_range(p)

 >

Update

Warning.  plottools:-getdata(p,'rangesonly') is buggy. I replaced this with

rhs~(indets(p, identical("originalview")=anything))[];

which gives more accurate Y ranges used. Here is example showing that getdata(p,'rangesonly') returns wrong y ranges for a plot compared to how it shows on the screen, So in the function above, better use the second method instead. This whole getdata(p,'rangesonly'); should be looked at by Maplesoft and fix to make it return correct values that agrees with screen view.

 > sol:=1/2/cos(x)*(sin(x)^2+(sin(x)^4+36*cos(x))^(1/2)); p:=plot(sol,x=-3..3);

 > plottools:-getdata(p,'rangesonly'); #WRONG y values compared to the above plot

 > rhs~(indets(p, identical("originalview")=anything))[]; #better result compared to plot (still not exact but better).

 >