Wrong calculation in Tikz foreach
Clash Royale CLAN TAG#URR8PPP
up vote
3
down vote
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I've a misunderstanding about the method Tikz compute some numbers. I draw a graph with some scale
. Here is a MWE :
documentclassstandalone
usepackage[french]babel
usepackagetikz
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
foreach t in 0, 0.08, ..., 0.48%
draw (t,1) -- (t,-1) node[below]t;
endtikzpicture
enddocument
I thought 0.08 x 5 = 0.40
and not 0.40001
. And why the number 0.48 does not appear ?
I guess the xscale
factor is not foreign by this problem but i can't address the problem by changing this factor. Otherwise i have a coefficient in all the following graphplots.
I read on this post that pgf
has a uniform relative precision of about 4âÂÂ5 correct digits. Is it the same for Tikz ? Is there a way to increase the precision of Tikz ?
Thx for you help !
tikz-pgf foreach
add a comment |Â
up vote
3
down vote
favorite
I've a misunderstanding about the method Tikz compute some numbers. I draw a graph with some scale
. Here is a MWE :
documentclassstandalone
usepackage[french]babel
usepackagetikz
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
foreach t in 0, 0.08, ..., 0.48%
draw (t,1) -- (t,-1) node[below]t;
endtikzpicture
enddocument
I thought 0.08 x 5 = 0.40
and not 0.40001
. And why the number 0.48 does not appear ?
I guess the xscale
factor is not foreign by this problem but i can't address the problem by changing this factor. Otherwise i have a coefficient in all the following graphplots.
I read on this post that pgf
has a uniform relative precision of about 4âÂÂ5 correct digits. Is it the same for Tikz ? Is there a way to increase the precision of Tikz ?
Thx for you help !
tikz-pgf foreach
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I've a misunderstanding about the method Tikz compute some numbers. I draw a graph with some scale
. Here is a MWE :
documentclassstandalone
usepackage[french]babel
usepackagetikz
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
foreach t in 0, 0.08, ..., 0.48%
draw (t,1) -- (t,-1) node[below]t;
endtikzpicture
enddocument
I thought 0.08 x 5 = 0.40
and not 0.40001
. And why the number 0.48 does not appear ?
I guess the xscale
factor is not foreign by this problem but i can't address the problem by changing this factor. Otherwise i have a coefficient in all the following graphplots.
I read on this post that pgf
has a uniform relative precision of about 4âÂÂ5 correct digits. Is it the same for Tikz ? Is there a way to increase the precision of Tikz ?
Thx for you help !
tikz-pgf foreach
I've a misunderstanding about the method Tikz compute some numbers. I draw a graph with some scale
. Here is a MWE :
documentclassstandalone
usepackage[french]babel
usepackagetikz
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
foreach t in 0, 0.08, ..., 0.48%
draw (t,1) -- (t,-1) node[below]t;
endtikzpicture
enddocument
I thought 0.08 x 5 = 0.40
and not 0.40001
. And why the number 0.48 does not appear ?
I guess the xscale
factor is not foreign by this problem but i can't address the problem by changing this factor. Otherwise i have a coefficient in all the following graphplots.
I read on this post that pgf
has a uniform relative precision of about 4âÂÂ5 correct digits. Is it the same for Tikz ? Is there a way to increase the precision of Tikz ?
Thx for you help !
tikz-pgf foreach
tikz-pgf foreach
asked 33 mins ago
Piroooh
558
558
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add a comment |Â
3 Answers
3
active
oldest
votes
up vote
4
down vote
accepted
The Tikz manual states that this is normal, and I quote (p 902):
Normally, when a list item
...
is encountered, there should already
have been two list items before it, which where numbers. Examples of
numbers are 1, -10, or -0.24. Let us call these numbersx
andy
and
letd := y â x
be their difference. Next, there should also be one
number following the three dots, let us call this numberz
.
In this situation, the part of the list reading
x,y,...,z
is replaced byx, x + d, x + 2d, x + 3d, ..., x + md
where the last dots are semantic
dots, not syntactic dots. The value m is the largest number such that
x + md ⤠z
if d is positive or such thatx + md âÂÂ¥ z
if d is negative.
Perhaps it is best to explain this by some examples: The following
<list>
have the same effects:
foreach x in 1,2,...,6 x, yields 1, 2, 3, 4, 5, 6
foreach x in 1,2,3,...,6 x, yields 1, 2, 3, 4, 5, 6
foreach x in 1,3,...,11 x, yields 1, 3, 5, 7, 9, 11
foreach x in 1,3,...,10 x, yields 1, 3, 5, 7, 9
foreach x in 0,0.1,...,0.5 x, yields 0, 0.1, 0.20001, 0.30002, 0.40002
foreach x in a,b,9,8,...,1,2,2.125,...,2.5 x, yields a, b, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 2.125, 2.25, 2.375, 2.5
Like you, I asked myself the question and @egreg answered it excellently here: Why does pgffor estimate that 0.1-0=0.100005 in a foreach loop?
Very nice, in fact it's due to the decimal values and not thescale
factor ! I read the p.675 in the pgf-tikz manual who is the same than what you have quoted and the answer of @egreg. A way is simply to erase the dots and to write the numbers one-by-one. Easy for 5 values, less convenient for a bigger sample. Thx to quote the Tikz manual and the corresponding topic !
â Piroooh
7 mins ago
Yes, and @RuixiZhang gives a way to keep the accuracy of calculations with aforeach
loop in his answer here: tex.stackexchange.com/a/446027/138900
â AndréC
4 mins ago
add a comment |Â
up vote
2
down vote
The limited precision is the obstacle.
You can get much greater accuracy using expl3
.
documentclassstandalone
usepackagetikz
usepackagexparse
ExplSyntaxOn
NewDocumentCommandfpforeachmmmm
% #1 = start, #2 = step, #3 = end, #4 = what to do
fp_step_inline:nnnn #1 #2 #3 #4
ExplSyntaxOff
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
fpforeach00.080.48
draw (#1,1) -- (#1,-1) node[below]#1;
endtikzpicture
enddocument
Beware of divisions, though, because the problems are still there and the final step might be missing due to accuracy issues nonetheless, but this is a problem with all floating point computations.
add a comment |Â
up vote
1
down vote
You can fix this by first working with integers and then reformatting the numbers to be the decimal representation you'd like to have:
First, I set the precision for the floating point
pgfkeys/pgf/number format/precision=2
Then in the foreach
loop I parse the integers to become the desired decimals using the following code
pgfmathparset/100
pgfmathroundtozerofillpgfmathresult
pgfmathsetmacrotpgfmathresult
Here's the full code:
documentclassstandalone
usepackage[french]babel
usepackagetikz
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
pgfkeys/pgf/number format/precision=2
foreach t in 0, 8, ..., 48
pgfmathparset/100
pgfmathroundtozerofillpgfmathresult
pgfmathsetmacrotpgfmathresult
draw (t,1) -- (t,-1)
node[below]
t;
endtikzpicture
enddocument
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
accepted
The Tikz manual states that this is normal, and I quote (p 902):
Normally, when a list item
...
is encountered, there should already
have been two list items before it, which where numbers. Examples of
numbers are 1, -10, or -0.24. Let us call these numbersx
andy
and
letd := y â x
be their difference. Next, there should also be one
number following the three dots, let us call this numberz
.
In this situation, the part of the list reading
x,y,...,z
is replaced byx, x + d, x + 2d, x + 3d, ..., x + md
where the last dots are semantic
dots, not syntactic dots. The value m is the largest number such that
x + md ⤠z
if d is positive or such thatx + md âÂÂ¥ z
if d is negative.
Perhaps it is best to explain this by some examples: The following
<list>
have the same effects:
foreach x in 1,2,...,6 x, yields 1, 2, 3, 4, 5, 6
foreach x in 1,2,3,...,6 x, yields 1, 2, 3, 4, 5, 6
foreach x in 1,3,...,11 x, yields 1, 3, 5, 7, 9, 11
foreach x in 1,3,...,10 x, yields 1, 3, 5, 7, 9
foreach x in 0,0.1,...,0.5 x, yields 0, 0.1, 0.20001, 0.30002, 0.40002
foreach x in a,b,9,8,...,1,2,2.125,...,2.5 x, yields a, b, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 2.125, 2.25, 2.375, 2.5
Like you, I asked myself the question and @egreg answered it excellently here: Why does pgffor estimate that 0.1-0=0.100005 in a foreach loop?
Very nice, in fact it's due to the decimal values and not thescale
factor ! I read the p.675 in the pgf-tikz manual who is the same than what you have quoted and the answer of @egreg. A way is simply to erase the dots and to write the numbers one-by-one. Easy for 5 values, less convenient for a bigger sample. Thx to quote the Tikz manual and the corresponding topic !
â Piroooh
7 mins ago
Yes, and @RuixiZhang gives a way to keep the accuracy of calculations with aforeach
loop in his answer here: tex.stackexchange.com/a/446027/138900
â AndréC
4 mins ago
add a comment |Â
up vote
4
down vote
accepted
The Tikz manual states that this is normal, and I quote (p 902):
Normally, when a list item
...
is encountered, there should already
have been two list items before it, which where numbers. Examples of
numbers are 1, -10, or -0.24. Let us call these numbersx
andy
and
letd := y â x
be their difference. Next, there should also be one
number following the three dots, let us call this numberz
.
In this situation, the part of the list reading
x,y,...,z
is replaced byx, x + d, x + 2d, x + 3d, ..., x + md
where the last dots are semantic
dots, not syntactic dots. The value m is the largest number such that
x + md ⤠z
if d is positive or such thatx + md âÂÂ¥ z
if d is negative.
Perhaps it is best to explain this by some examples: The following
<list>
have the same effects:
foreach x in 1,2,...,6 x, yields 1, 2, 3, 4, 5, 6
foreach x in 1,2,3,...,6 x, yields 1, 2, 3, 4, 5, 6
foreach x in 1,3,...,11 x, yields 1, 3, 5, 7, 9, 11
foreach x in 1,3,...,10 x, yields 1, 3, 5, 7, 9
foreach x in 0,0.1,...,0.5 x, yields 0, 0.1, 0.20001, 0.30002, 0.40002
foreach x in a,b,9,8,...,1,2,2.125,...,2.5 x, yields a, b, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 2.125, 2.25, 2.375, 2.5
Like you, I asked myself the question and @egreg answered it excellently here: Why does pgffor estimate that 0.1-0=0.100005 in a foreach loop?
Very nice, in fact it's due to the decimal values and not thescale
factor ! I read the p.675 in the pgf-tikz manual who is the same than what you have quoted and the answer of @egreg. A way is simply to erase the dots and to write the numbers one-by-one. Easy for 5 values, less convenient for a bigger sample. Thx to quote the Tikz manual and the corresponding topic !
â Piroooh
7 mins ago
Yes, and @RuixiZhang gives a way to keep the accuracy of calculations with aforeach
loop in his answer here: tex.stackexchange.com/a/446027/138900
â AndréC
4 mins ago
add a comment |Â
up vote
4
down vote
accepted
up vote
4
down vote
accepted
The Tikz manual states that this is normal, and I quote (p 902):
Normally, when a list item
...
is encountered, there should already
have been two list items before it, which where numbers. Examples of
numbers are 1, -10, or -0.24. Let us call these numbersx
andy
and
letd := y â x
be their difference. Next, there should also be one
number following the three dots, let us call this numberz
.
In this situation, the part of the list reading
x,y,...,z
is replaced byx, x + d, x + 2d, x + 3d, ..., x + md
where the last dots are semantic
dots, not syntactic dots. The value m is the largest number such that
x + md ⤠z
if d is positive or such thatx + md âÂÂ¥ z
if d is negative.
Perhaps it is best to explain this by some examples: The following
<list>
have the same effects:
foreach x in 1,2,...,6 x, yields 1, 2, 3, 4, 5, 6
foreach x in 1,2,3,...,6 x, yields 1, 2, 3, 4, 5, 6
foreach x in 1,3,...,11 x, yields 1, 3, 5, 7, 9, 11
foreach x in 1,3,...,10 x, yields 1, 3, 5, 7, 9
foreach x in 0,0.1,...,0.5 x, yields 0, 0.1, 0.20001, 0.30002, 0.40002
foreach x in a,b,9,8,...,1,2,2.125,...,2.5 x, yields a, b, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 2.125, 2.25, 2.375, 2.5
Like you, I asked myself the question and @egreg answered it excellently here: Why does pgffor estimate that 0.1-0=0.100005 in a foreach loop?
The Tikz manual states that this is normal, and I quote (p 902):
Normally, when a list item
...
is encountered, there should already
have been two list items before it, which where numbers. Examples of
numbers are 1, -10, or -0.24. Let us call these numbersx
andy
and
letd := y â x
be their difference. Next, there should also be one
number following the three dots, let us call this numberz
.
In this situation, the part of the list reading
x,y,...,z
is replaced byx, x + d, x + 2d, x + 3d, ..., x + md
where the last dots are semantic
dots, not syntactic dots. The value m is the largest number such that
x + md ⤠z
if d is positive or such thatx + md âÂÂ¥ z
if d is negative.
Perhaps it is best to explain this by some examples: The following
<list>
have the same effects:
foreach x in 1,2,...,6 x, yields 1, 2, 3, 4, 5, 6
foreach x in 1,2,3,...,6 x, yields 1, 2, 3, 4, 5, 6
foreach x in 1,3,...,11 x, yields 1, 3, 5, 7, 9, 11
foreach x in 1,3,...,10 x, yields 1, 3, 5, 7, 9
foreach x in 0,0.1,...,0.5 x, yields 0, 0.1, 0.20001, 0.30002, 0.40002
foreach x in a,b,9,8,...,1,2,2.125,...,2.5 x, yields a, b, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 2.125, 2.25, 2.375, 2.5
Like you, I asked myself the question and @egreg answered it excellently here: Why does pgffor estimate that 0.1-0=0.100005 in a foreach loop?
answered 19 mins ago
AndréC
3,661729
3,661729
Very nice, in fact it's due to the decimal values and not thescale
factor ! I read the p.675 in the pgf-tikz manual who is the same than what you have quoted and the answer of @egreg. A way is simply to erase the dots and to write the numbers one-by-one. Easy for 5 values, less convenient for a bigger sample. Thx to quote the Tikz manual and the corresponding topic !
â Piroooh
7 mins ago
Yes, and @RuixiZhang gives a way to keep the accuracy of calculations with aforeach
loop in his answer here: tex.stackexchange.com/a/446027/138900
â AndréC
4 mins ago
add a comment |Â
Very nice, in fact it's due to the decimal values and not thescale
factor ! I read the p.675 in the pgf-tikz manual who is the same than what you have quoted and the answer of @egreg. A way is simply to erase the dots and to write the numbers one-by-one. Easy for 5 values, less convenient for a bigger sample. Thx to quote the Tikz manual and the corresponding topic !
â Piroooh
7 mins ago
Yes, and @RuixiZhang gives a way to keep the accuracy of calculations with aforeach
loop in his answer here: tex.stackexchange.com/a/446027/138900
â AndréC
4 mins ago
Very nice, in fact it's due to the decimal values and not the
scale
factor ! I read the p.675 in the pgf-tikz manual who is the same than what you have quoted and the answer of @egreg. A way is simply to erase the dots and to write the numbers one-by-one. Easy for 5 values, less convenient for a bigger sample. Thx to quote the Tikz manual and the corresponding topic !â Piroooh
7 mins ago
Very nice, in fact it's due to the decimal values and not the
scale
factor ! I read the p.675 in the pgf-tikz manual who is the same than what you have quoted and the answer of @egreg. A way is simply to erase the dots and to write the numbers one-by-one. Easy for 5 values, less convenient for a bigger sample. Thx to quote the Tikz manual and the corresponding topic !â Piroooh
7 mins ago
Yes, and @RuixiZhang gives a way to keep the accuracy of calculations with a
foreach
loop in his answer here: tex.stackexchange.com/a/446027/138900â AndréC
4 mins ago
Yes, and @RuixiZhang gives a way to keep the accuracy of calculations with a
foreach
loop in his answer here: tex.stackexchange.com/a/446027/138900â AndréC
4 mins ago
add a comment |Â
up vote
2
down vote
The limited precision is the obstacle.
You can get much greater accuracy using expl3
.
documentclassstandalone
usepackagetikz
usepackagexparse
ExplSyntaxOn
NewDocumentCommandfpforeachmmmm
% #1 = start, #2 = step, #3 = end, #4 = what to do
fp_step_inline:nnnn #1 #2 #3 #4
ExplSyntaxOff
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
fpforeach00.080.48
draw (#1,1) -- (#1,-1) node[below]#1;
endtikzpicture
enddocument
Beware of divisions, though, because the problems are still there and the final step might be missing due to accuracy issues nonetheless, but this is a problem with all floating point computations.
add a comment |Â
up vote
2
down vote
The limited precision is the obstacle.
You can get much greater accuracy using expl3
.
documentclassstandalone
usepackagetikz
usepackagexparse
ExplSyntaxOn
NewDocumentCommandfpforeachmmmm
% #1 = start, #2 = step, #3 = end, #4 = what to do
fp_step_inline:nnnn #1 #2 #3 #4
ExplSyntaxOff
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
fpforeach00.080.48
draw (#1,1) -- (#1,-1) node[below]#1;
endtikzpicture
enddocument
Beware of divisions, though, because the problems are still there and the final step might be missing due to accuracy issues nonetheless, but this is a problem with all floating point computations.
add a comment |Â
up vote
2
down vote
up vote
2
down vote
The limited precision is the obstacle.
You can get much greater accuracy using expl3
.
documentclassstandalone
usepackagetikz
usepackagexparse
ExplSyntaxOn
NewDocumentCommandfpforeachmmmm
% #1 = start, #2 = step, #3 = end, #4 = what to do
fp_step_inline:nnnn #1 #2 #3 #4
ExplSyntaxOff
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
fpforeach00.080.48
draw (#1,1) -- (#1,-1) node[below]#1;
endtikzpicture
enddocument
Beware of divisions, though, because the problems are still there and the final step might be missing due to accuracy issues nonetheless, but this is a problem with all floating point computations.
The limited precision is the obstacle.
You can get much greater accuracy using expl3
.
documentclassstandalone
usepackagetikz
usepackagexparse
ExplSyntaxOn
NewDocumentCommandfpforeachmmmm
% #1 = start, #2 = step, #3 = end, #4 = what to do
fp_step_inline:nnnn #1 #2 #3 #4
ExplSyntaxOff
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
fpforeach00.080.48
draw (#1,1) -- (#1,-1) node[below]#1;
endtikzpicture
enddocument
Beware of divisions, though, because the problems are still there and the final step might be missing due to accuracy issues nonetheless, but this is a problem with all floating point computations.
answered 11 mins ago
egreg
688k8518323080
688k8518323080
add a comment |Â
add a comment |Â
up vote
1
down vote
You can fix this by first working with integers and then reformatting the numbers to be the decimal representation you'd like to have:
First, I set the precision for the floating point
pgfkeys/pgf/number format/precision=2
Then in the foreach
loop I parse the integers to become the desired decimals using the following code
pgfmathparset/100
pgfmathroundtozerofillpgfmathresult
pgfmathsetmacrotpgfmathresult
Here's the full code:
documentclassstandalone
usepackage[french]babel
usepackagetikz
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
pgfkeys/pgf/number format/precision=2
foreach t in 0, 8, ..., 48
pgfmathparset/100
pgfmathroundtozerofillpgfmathresult
pgfmathsetmacrotpgfmathresult
draw (t,1) -- (t,-1)
node[below]
t;
endtikzpicture
enddocument
add a comment |Â
up vote
1
down vote
You can fix this by first working with integers and then reformatting the numbers to be the decimal representation you'd like to have:
First, I set the precision for the floating point
pgfkeys/pgf/number format/precision=2
Then in the foreach
loop I parse the integers to become the desired decimals using the following code
pgfmathparset/100
pgfmathroundtozerofillpgfmathresult
pgfmathsetmacrotpgfmathresult
Here's the full code:
documentclassstandalone
usepackage[french]babel
usepackagetikz
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
pgfkeys/pgf/number format/precision=2
foreach t in 0, 8, ..., 48
pgfmathparset/100
pgfmathroundtozerofillpgfmathresult
pgfmathsetmacrotpgfmathresult
draw (t,1) -- (t,-1)
node[below]
t;
endtikzpicture
enddocument
add a comment |Â
up vote
1
down vote
up vote
1
down vote
You can fix this by first working with integers and then reformatting the numbers to be the decimal representation you'd like to have:
First, I set the precision for the floating point
pgfkeys/pgf/number format/precision=2
Then in the foreach
loop I parse the integers to become the desired decimals using the following code
pgfmathparset/100
pgfmathroundtozerofillpgfmathresult
pgfmathsetmacrotpgfmathresult
Here's the full code:
documentclassstandalone
usepackage[french]babel
usepackagetikz
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
pgfkeys/pgf/number format/precision=2
foreach t in 0, 8, ..., 48
pgfmathparset/100
pgfmathroundtozerofillpgfmathresult
pgfmathsetmacrotpgfmathresult
draw (t,1) -- (t,-1)
node[below]
t;
endtikzpicture
enddocument
You can fix this by first working with integers and then reformatting the numbers to be the decimal representation you'd like to have:
First, I set the precision for the floating point
pgfkeys/pgf/number format/precision=2
Then in the foreach
loop I parse the integers to become the desired decimals using the following code
pgfmathparset/100
pgfmathroundtozerofillpgfmathresult
pgfmathsetmacrotpgfmathresult
Here's the full code:
documentclassstandalone
usepackage[french]babel
usepackagetikz
begindocument
begintikzpicture[yscale=0.1,xscale=25]
draw[<->] (0.5,0) node[below right]t -- (0,0) -- (0,100) node[above left]x(t);
%%Graduation
pgfkeys/pgf/number format/precision=2
foreach t in 0, 8, ..., 48
pgfmathparset/100
pgfmathroundtozerofillpgfmathresult
pgfmathsetmacrotpgfmathresult
draw (t,1) -- (t,-1)
node[below]
t;
endtikzpicture
enddocument
answered 7 mins ago
A.Ellett
35.4k1064164
35.4k1064164
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