"But will it be relevant?"--Barry Dayton

The book is now out in Kindle, paperback and notebook formats from Wolfram Media. Go to wolfr.am/DaytonCurves for current information and links.

In addition there is a free summary of the book in Wolfram's *The Mathematica Journal*.

A Wolfram Language approach to Real Numerical Algebraic Plane Curves (PDF 3.4 MB)

This article is also available in notebook (.nb) and Wolfram Reader (.cdf) format. The global functions used in this article are available in Mathematica notebook form. These can be executed in Mathematica. If you do not have access to Mathematica and just want to look at the full code you can read this notebook using the free Wolfram CDF player.

For those readers of the TMJ article who might want to get more information on a particular chapter individual chapter notebooks and additional material are available for download at Chapter Notebooks and More. If you want more than a few a better option is to to the Wolfram media link above and download the zip file. You do need to download the Appendix 2, Global Functions (.nb 1.1MB) notebook and Evaluate initialization cells before using any of the other notebooks.

For the convenience of all users of the software defined in this book we have an index to Global Functions (PDF) which lists all the Global Functions (Appendix 2) alphabetically, giving syntax and location, by section, where further information on this function can be found in the book, chapter notebooks or Global Function notebook.

One challenge in production of this book is that both the typesetting an execution of code is done by Mathematica at the same time. For technical reasons some code did not execute properly when the the fixed print versions were typeset. These will run correctly in the notebook versions if properly initialized, you may need to re-run them from the downloaded files. Here are corrections:

**Section 1.6 page 16**(Make sure for`In[46] the cell property "evaluatable" is set.)`

`In[46] gs = sqFree[g, x, y, 1.*^-12]`

Out[46] 0.132808 x - 0.132808 x^3 - 0.132808 y + 0.132808 x^2 y - 0.132808 x y^2 + 0.132808 y^3`In[48] gs = Expand[gs/Coefficient[gs, x^3]]`

Out[48] -1. x + 1. x^3 + 1. y - 1. x^2 y + 1. x y^2 - 1. y^3**Section 3.2, page 45**(computer error)

`In[18] run2 = tangentRealPoints[f, k, x, y]`

Out[18] {{1.15237, 1.27611}, {0.707107, 0.5}, {0.707107, 0.5}, {0., -0.5}, {0., -0.5}, {0.928493, -0.857753}, {-0.754479, 0.417765}, {-0.707107, 0.5}, {-0.707107, 0.5}}**Section 3.4, page 50**(failure to update from earlier version)`In[50] fbow = x^4 - x^2 y + y^3;`

fmin = -x^2 y + y^3;

infiniteRealPoints[fmin, x, y]

Out[50] {{-5.22164, -5.22164, 0}, {-4.1098, 0., 0}, {-3.38833, 3.38833, 0}}**Section 3.5,page 53**(failure to update)`In[69] fm1 = Factor[pointMinForm[f, {-2, 0}, x, y]]`

Out[69] 16 (x - y) (x + y)`In[71] fm2 = Factor[pointMinForm[f, {2, 0}, x, y]]`

Out[71] 16 (x - y) (x + y)**Section 5.3, pages 98-99**(Make sure`dTol = 1.*^-12)`

`In[22] intersectionMultiplicity[y - x^2 + 1, y^2 - x^2 - 5, {2, 3}, dTol]`

Out[22] 1In[23] intersectionMultiplicity[y + 1/3 x^2 - 2 x - 1/3, y^2 - x^2 - 5, {2, 3}, dTol]

Out[23] 2In[24] intersectionMultiplicity[y - x^3, y, {0, 0}, dTol]

Out[24] 3In[26] intersectionMultiplicity[y - x - x^3, y - x - y^3, {0, 0}, dTol]

Out[26] 5In[27] intersectionMultiplicity[y^2 - x^3, y - 3 x, {0, 0}, dTol]

Out[27] 2`In[28] intersectionMultiplicity[x^2 + y^2, y - 3 x, {0, 0}, dTol]`

Out[28] 2**Section 7.6, p.167**(Failure to update from earlier version)

`In[165] {intersectionMultiplicity[y^2 - x^3 - x^2, l, {0, 0}, dTol],`

intersectionMultiplicity[y^2 - x^3, l, {0, 0}, dTol],

intersectionMultiplicity[(y - x^2) (y + x^4), l, {0, 0}, dTol],

intersectionMultiplicity[x y (x - y), l, {0, 0}, dTol]}

Out[165] {2, 2, 2, 3}Below this the variable

`d`was assumed non-initialized but apparently was. The correction is

`In[166] Clear[d]`

Expand[(d-1)(d-2)/2+2d-3]

Out[166] -2+d/2+d^2/2On page 168 we have the same problem. Hopefully now

`d`is unevaluated so

`In[167] Expand[2((d-1)(d-2)/2)+2d-3]`

But this is

Out[167] -1-d+d^2

`d(d-1)-1.`**Section 8.5 p.194-195**The graphic for Example 3 was omitted. It does appear on p. 206. For original notebook version this is also a problem, the picture is in Section 8.7.**Section 8.7 p. 204 Example A2**The graphic for Example A2, affine hyperbola, is wrong, the correct picture was shown on p 194. This can be corrected in the notebook version by changing the first line of in[169] to`Hp = Table[{Sqrt[y^2 + 4], y}, {y, -6, 6, .201}]`

This avoids hitting the x-axis which is ambiguous.

Let me know at barry@barryhdayton.us if you find other places where there is a problem.