ReplaceAll not working properly

Question

Still early with Mathematica, please forgive me, which is probably a very obvious question. I am trying to create some parametric graphs. I have:

ParametricPlot[{
    (a + b) Cos[t] - h Cos[(a + b)/b t],
    (a + b) Sin[t] - h Sin[(a + b)/b t]},
    {t, 0, 2 \[Pi]}, PlotRange -> All] /. {a -> 2, b -> 1, h -> 1}

No joy: replacement rules do not apply a, band hremain undefined.

If I instead:

Hold@ParametricPlot[{
    (a + b) Cos[t] - h Cos[(a + b)/b t],
    (a + b) Sin[t] - h Sin[(a + b)/b t]},
    {t, 0, 2 \[Pi]}, PlotRange -> All] /. {a -> 2, b -> 1, h -> 1}

ARE rules seem to work, as evidenced by the output:

Hold[ParametricPlot[{(2 + 1) Cos[t] - 
1 Cos[(2 + 1) t], (2 + 1) Sin[t] - 1 Sin[(2 + 1) t]}, {t, 0, 
2 \[Pi]}, PlotRange -> All]]

This is what I expected. However, release Hold, but ParametricPlotdoes not work. However, there is nothing wrong with the equations or ParametricPlotmyself, because I tried to set the values ​​for a, b and h in a separate expression ( a=2; b=1; h=1), and I will get my pretty double cardioid as expected.

, ReplaceAll ? , - .

ReplaceAll ParametricPlot, , , , "ParametricPlot HoldAll f ", , .

.

Answer 1

Mathematica , . ReplaceAll , ParametricPlot Graphics

,

ParametricPlot[{(a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - 
      h Sin[(a + b)/b t]}, {t, 0, 2 \[Pi]}, 
    PlotRange -> All] /. {a -> 2, b -> 1, h -> 1} // Hold // TreeForm

, ,

temp1=ParametricPlot[{(a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - 
          h Sin[(a + b)/b t]}, {t, 0, 2 \[Pi]}, 
        PlotRange -> All]
temp2={a -> 2, b -> 1, h -> 1} 
temp1/.temp2

FullForm[temp1], , a b.

ReplaceAll HoldFirst, ParametricPlot ReplaceAll, - , . ReplaceAll head ParametricPlot, ParametricPlot . , reset , .

SetAttributes[ReplaceAll, HoldFirst]; 
ParametricPlot[{(a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - 
    h Sin[(a + b)/b t]}, {t, 0, 2 \[Pi]}, 
  PlotRange -> All] /. {a -> 2, b -> 1, h -> 1}
ClearAttributes[ReplaceAll, HoldFirst]

, , HoldAll, List head ParametricPlot ,

ParametricPlot @@ ({{(a + b) Cos[t] - 
      h Cos[(a + b)/b t], (a + b) Sin[t] - h Sin[(a + b)/b t]}, {t, 0,
      2 \[Pi]}, PlotRange -> All} /. {a -> 2, b -> 1, h -> 1})

Answer 2

ReplaceAll.

. :

In[10]:= (a/a) /. a -> 0

Out[10]= 1  

, , :

In[11]:= a = 0; a/a

During evaluation of In[11]:= Power::infy: Infinite expression 1/0 encountered. >>

During evaluation of In[11]:= Infinity::indet: Indeterminate expression 0 ComplexInfinity encountered. >>

Out[12]= Indeterminate  

, , . "" , , . :

ParametricPlot[
   {(a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - h Sin[(a + b)/b t]} 
   /. {a -> 2, b -> 1, h -> 1},
   {t, 0, 2 \[Pi]}, 

 PlotRange -> All
]

Answer 3

Mathematica - Module[]:

Module[{a = 2, b = 1, h = 1}, 
   ParametricPlot[{(a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - h Sin[(a + b)/b t]}, 
   {t, 0, 2 \[Pi]}, 
   PlotRange -> All]]

, a, b h , Module. , ReleaseHold , :

ReleaseHold[
   Hold@ParametricPlot[{(a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - h Sin[(a + b)/b t]}, 
   {t, 0, 2 \[Pi]}, 
   PlotRange -> All] /. {a -> 2, b -> 1, h -> 1}]

EDIT:. . , , HoldAll ( ). , Hold, ( ), , ( , - ) HoldAll .

In[1]  := Hold[a /. a -> 5]
Out[1] := Hold[a /. a -> 5]
In[2]  := Hold[a] /. a -> 5
Out[2] := Hold[5]

, Hold HoldAll , , ParametricPlot HoldAll .: - (

EDIT2: Trace, , , , ReplaceAll , ParametricPlot ( a, b h). Hold[a] /. a -> 5 Hold[a], .

Answer 4

, .

f[t_] := {(a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - 
   h Sin[(a + b)/b t]}

1:

Module[{a = 2, b = 1, h = 1}, 
 ParametricPlot[f[t], {t, 0, 2 \[Pi]}, PlotRange -> All]]

2:

Module[{a = 2, b = 1, h = 1}, 
 ParametricPlot[Evaluate[f[t]], {t, 0, 2 \[Pi]}, PlotRange -> All]]

( 3)

ParametricPlot[
 Module[{a = 2, b = 1, h = 1}, Evaluate[f[t]]], {t, 0, 2 \[Pi]}, 
 PlotRange -> All]

( 4)

Module[{a = 2, b = 1, h = 1}, 
   ParametricPlot[{(a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - h Sin[(a + b)/b t]}, 
   {t, 0, 2 \[Pi]}, 
   PlotRange -> All]]

- , 4, 2 ? ( , ).

, :

ParametricPlot[
 Evaluate[{(a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - 
     h Sin[(a + b)/b t]}] /. {a -> 2, b -> 1, h -> 1}, {t, 0, 
  2 \[Pi]}, PlotRange -> All]

f[x_] := (a x)/(b + x);
With[{a = 10, b = 100}, Plot[Evaluate[f[x]], {x, 0, 100}]]
With[{a = 10, b = 100}, Plot[(a x)/(b + x), {x, 0, 100}]]
Plot[With[{a = 10, b = 100}, Evaluate[f[x]]], {x, 0, 100}]
Plot[Evaluate[f[x]] /. {a -> 10, b -> 100}, {x, 0, 100}]

1 (Edit) ( "Plot" x , "Block"?)

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