Questions in category: Calculator (Calculator)

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1. 使用 Sowya 计算 sin(x)

Posted by haifeng on 2023-12-21 11:00:47 last update 2023-12-21 11:01:43 | Answers (0) | 收藏

$\sin(x)$ 的 Taylor 展开（见问题2722）为

$\sin x=x-\frac{1}{3!}x^3+\frac{1}{5!}x^5-\frac{1}{7!}x^7+\cdots+(-1)^{n}\frac{1}{(2n+1)!}x^{2n+1}+\cdots$

>> setprecision(100)
Now the precision is: 100

------------------------

>> sum((-1)^n/((2*n+1)!),n,0,10)
0.8414709848078965066525409389542263831247347547521504910395056013623995289262652434908558497261901517
------------------------

>> sum((-1)^n/((2*n+1)!),n,0,100)
0.8414709848078965066525023216302989996225630607983710656727517099919104043912396689486397435430526956
------------------------

2. 计算 $1*2*3+3*4*5+5*6*7+\cdots+99*100*101$ 的值.

Posted by haifeng on 2023-10-24 18:56:39 last update 2023-10-24 18:58:10 | Answers (0) | 收藏

>> sum((2*k-1)*(2*k)*(2*k+1),k,1,50)
13002450
------------------------

3. 求解下列一元二次方程

Posted by haifeng on 2023-08-30 08:14:03 last update 2023-08-31 08:36:07 | Answers (3) | 收藏

(1)   $112y^2+16y-7.68=0$

(2)   $112x^2+16x-7=0$

(3)    $x^2-14x-232=0$

4. Calculator 的新名字

Posted by haifeng on 2023-02-26 22:30:04 last update 2023-04-05 19:14:04 | Answers (0) | 收藏

Calculator 是计算器的意思, 是十分普通的. 因此应该起个比较特别的名字.

Souya,  数学的吴音.  或者 Sowya, 法语发音比较接近吴语中的“数学”发音.

THL ,  maTH Language.  THL 也为了纪念家乡.

5. 利用递推公式求定积分 $I_n=\int_0^1 \frac{x^n}{x+5}\mathrm{d}x$.

Posted by haifeng on 2023-02-24 22:33:00 last update 2023-02-28 15:21:33 | Answers (1) | 收藏

$I_n=-5*I_{n-1}+\frac{1}{n}$

$\begin{split} I_n&=\int_0^1 \frac{x^n}{x+5}\mathrm{d}x=\int_0^1 \frac{x^{n-1}(x+5)-5x^{n-1}}{x+5}\mathrm{d}x\\ &=\int_0^1 x^{n-1}\mathrm{d}x-5\int_0^1 \frac{x^{n-1}}{x+5}\mathrm{d}x\\ &=\frac{1}{n}x^n\biggr|_0^1 -5I_{n-1}\\ &=\frac{1}{n}-5I_{n-1}. \end{split}$

>> setprecision(20)
in> setprecision(20)
Now the precision is: 20

------------------------

>> printRecursiveSeries(-5*I_k+1/(k+1),I_k,0.0883922160302268689414,20,\n,linenumber)
in> printRecursiveSeries(0-5*I_k+1/(k+1),I_k,0.0883922160302268689414,20,\n,linenumber)
【1】 0.0883922160302268689414
【2】 0.0580389198488656552930
【3】 0.0431387340890050568650
【4】 0.0343063295549747156750
【5】 0.0284683522251264216250
【6】 0.0243249055410345585450
【7】 0.0212326151519700644150
【8】 0.0188369242401496779250
【9】 0.0169264899103627214850
【10】 0.0153675504481863925750
【11】 0.0140713386681589462150
【12】 0.0129766399925386022550
【13】 0.0120398769603839118050
【14】 0.0112291866266518695450
【15】 0.0105207335334073189450
【16】 0.0098963323329634052750
【17】 0.0093418677469476795050
【18】 0.0088462168208171580350
【19】 0.0084004948432826308750
【20】 0.0079975257835868456250

----------------
By Calculator

https://zhuanlan.zhihu.com/p/566572045

6. register code

Posted by haifeng on 2023-02-22 19:56:51 last update 2023-02-23 22:04:52 | Answers (0) | 收藏

in> register(code)

This is the register code:

706f02c662ef45331a51abcd2b7dc3cfbe27bccf5bc57d02b751f22820b7d718

>>

atzjg, 2023-2-22

7. [Calculator] 关于递推公式的计算

Posted by haifeng on 2023-02-04 14:18:28 last update 2023-02-04 14:18:28 | Answers (0) | 收藏

Hanoi 问题的递推关系为 $a_n=2a_{n-1}+1$, $a_1=1$.

>> printRecursiveSeries(2*n+1,n,1,10,\n)
in> printRecursiveSeries(2*n+1,n,1,10,\n)
3
7
15
31
63
127
255
511
1023
2047

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>> printRecursiveSeries(2n+1,n,1,10,\n)
in> printRecursiveSeries(2n+1,n,1,10,\n)
22
223
2224
22225
222226
2222227
22222228
222222229
2222222230
22222222231

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8. [Calculator]

Posted by haifeng on 2023-02-03 19:10:05 last update 2023-02-04 10:08:41 | Answers (0) | 收藏

------------------------

>> c=3
--------------------
>> a=1
--------------------
>> l=12
--------------------
>> u=21
--------------------
>> t=20
--------------------
>> o=15
--------------------
>> r=18
--------------------
>> c+a+l+c+u+l+a+t+o+r
in> 3+1+12+3+21+12+1+20+15+18

out> 106

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9. [Bug] Calculator 中关于 % 运算的 Bug

Posted by haifeng on 2022-09-21 11:40:26 last update 2022-09-21 11:40:26 | Answers (1) | 收藏

>> 3 * (2-6 %(3 -7))
in> 3*(2-6%(3-7))

out> 312

------------------------

>> 6%(-4)
in> 6%(-4)

out> -25

------------------------

>> 6%(4)
in> 6%(4)

out> 25

------------------------

>> 6%4
in> 6%4

out> 1

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10. 解不定方程 $7x+4y=1$.

Posted by haifeng on 2022-09-21 00:02:58 last update 2022-09-21 00:02:58 | Answers (0) | 收藏

>> IndefiniteEquation(7,4)
in> IndefiniteEquation(7,4)
Solve the equation: 7*x+4*y = 1
7==1*4+3
4==1*3+1
1 1
test: 1==4*2-7*1
4*2-7*1 == 1
x = -1+4t
y = 2-7t

-----------***---------

>> IndefiniteEquation(7,4;1)
in> IndefiniteEquation(7,4;1)
Solve the indefinite equation :
7*X1+4*X2 = 1

u1=1-3*u0
---------------
X1 = -1*u1+u0
X2 = -1*X1+u1

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