Re: Some questions about Axiom

Erik Eidsvig <[email protected]> Fri, 25 May 2018 16:21:56 +0200
Newsgroups gmane.comp.mathematics.axiom.general
Message-ID <CADb45ZXNtwC=LzfU1qdmEp=h_StiezQ8LzM9kvVy5iCd=FOH0Q@mail.gmail.com>
--===============2783309039192807344==
Content-Type: multipart/related; boundary="00000000000089c0f0056d087de1"

--00000000000089c0f0056d087de1
Content-Type: multipart/alternative; boundary="00000000000089c0ee056d087de0"

--00000000000089c0ee056d087de0
Content-Type: text/plain; charset="UTF-8"

Or just answer some of them if you have the time. I will read myself up,
but have not found a tutorium that covers these things.

2018-05-23 23:44 GMT+02:00 Erik Eidsvig <[email protected]>:

> Hi! I love this program and has put a lot of time reading the tutorials
> and used it a lot in short time. However, I have run into some issues. I
> hope you have time to answer them:) I have tried a lot of commands on each
> questions to find out for myself, but to make the mail more easy to read I
> will only include my questions.
>
> How do I find the n-root of a number?
>
> How do I solve inequalites?
>
> How do I find the angle in a scalar product? Degrees and radians.
>
> Is it possible to find the logarithm with base 10, 2 and 3 etc?
>
> How can I calculate easy logarithmic tasks like this: (I think I have read
> it in a tutorial, but I have searched and I can not find it)
>
>
>
> If I know the x-value of the function, is it possible to make Axiom find
> the tangent in this point?
>
> If I know the x-value of the function (vector) is it possible to make
> Axiom find the function of the line that stands normal on this point?
>
> Is it possible to find the distance between the line and a point?
>
> The lenght of a vector?
>
> Permutations and combinations in probability nCr and NPr?
>
> How can I rewrite a expression to with respect to a variable? For example
> v=H*r and to make axiom rewrite this as r=H/r?
>
> And I guess lcm is defined for only 2 numbers and not 3?
>
> I realize that this is a lot of questions, so it is completely okay if you
> answer each questions short. I have tried a lot on my own, but  need hints
> to understand the whole picture. I will also try to understand the coding
> of the programme afterwards:)It took me a short time to become natural with
> the programme, so thanks a lot!
>

--00000000000089c0ee056d087de0
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">Or just answer some of them if you have the time. I will r=
ead myself up, but have not found a tutorium that covers these things.</div=
><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">2018-05-23 23:44=
 GMT+02:00 Erik Eidsvig <span dir=3D"ltr">&lt;<a href=3D"mailto:eeidsvig@gm=
ail.com" target=3D"_blank">[email protected]</a>&gt;</span>:<br><blockquot=
e class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc sol=
id;padding-left:1ex"><div dir=3D"ltr">Hi! I love this program and has put a=
 lot of time reading the tutorials and used it a lot in short time. However=
, I have run into some issues. I hope you have time to answer them:) I have=
 tried a lot of commands on each questions to find out for myself, but to m=
ake the mail more easy to read I will only include my questions.<div><br></=
div><div>How do I find the n-root of a number?</div><div><br></div><div>How=
 do I solve inequalites?</div><div><br></div><div>How do I find the angle i=
n a scalar product? Degrees and radians.</div><div><br></div><div>Is it pos=
sible to find the logarithm with base 10, 2 and 3 etc?</div><div><br></div>=
<div>How can I calculate easy logarithmic tasks like this: (I think I have =
read it in a tutorial, but I have searched and I can not find it)</div><div=
><img src=3D"cid:ii_jhjmpmmg0_1638eef184094bac" width=3D"208" height=3D"49"=
 style=3D"margin-right:0px"><br><br></div><div><br></div><div>If I know the=
 x-value of the function, is it possible to make Axiom find the tangent in =
this point?</div><div><br></div><div>If I know the x-value of the function =
(vector) is it possible to make Axiom find the function of the line that st=
ands normal on this point?</div><div><br></div><div>Is it possible to find =
the distance between the line and a point?=C2=A0</div><div><br></div><div>T=
he lenght of a vector?</div><div><br></div><div>Permutations and combinatio=
ns in probability nCr and NPr?</div><div><br></div><div>How can I rewrite a=
 expression to with respect to a variable? For example v=3DH*r and to make =
axiom rewrite this as r=3DH/r?</div><div><br></div><div>And I guess lcm is =
defined for only 2 numbers and not 3?</div><div><br></div><div>I realize th=
at this is a lot of questions, so it is completely okay if you answer each =
questions short. I have tried a lot on my own, but=C2=A0 need hints to unde=
rstand the whole picture. I will also try to understand the coding of the p=
rogramme afterwards:)It took me a short time to become natural with the pro=
gramme, so thanks a lot!</div></div>
</blockquote></div><br></div>

--00000000000089c0ee056d087de0--
--00000000000089c0f0056d087de1
Content-Type: image/png; name="image.png"
Content-Disposition: inline; filename="image.png"
Content-Transfer-Encoding: base64
Content-ID: <ii_jhjmpmmg0_1638eef184094bac>
X-Attachment-Id: ii_jhjmpmmg0_1638eef184094bac
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==
--00000000000089c0f0056d087de1--


--===============2783309039192807344==
Content-Type: text/plain; charset="us-ascii"
MIME-Version: 1.0
Content-Transfer-Encoding: 7bit
Content-Disposition: inline

_______________________________________________
Axiom-math mailing list
[email protected]
https://lists.nongnu.org/mailman/listinfo/axiom-math

--===============2783309039192807344==--