In [94]:

    

#Julia()


    

In [1]:

    

using Symata


    

In [2]:

    

x1=Range(10.0^3)
y1=Range(10.0^3);


    

In [3]:

    

g(x_,y_):=Module([sum=0],
begin
    For(i=1, i<Length(x), i += 1,
        sum += x[i]^2 * y[i]^(-3))
    sum
end)


    

In [4]:

    

g(x1,y1)


    

    
Out[4]:





$$ 7.484470860550343 $$

In [5]:

    

resultsS1 = Timing(g(x1,y1))


    

    
Out[5]:





$$  \left[ 0.081327691,7.484470860550343 \right]  $$

In [6]:

    

Apply(Plus, x1^2/y1^3)


    

    
Out[6]:





$$ 7.485470860550343 $$

In [7]:

    

resultsS2=Timing(Apply(Plus, x1^2/y1^3))


    

    
Out[7]:





$$  \left[ 0.06112357,7.485470860550343 \right]  $$

In [8]:

    

jfunc = J( (x,y)->sum(u->u[1]^2/u[2]^(3), zip(x,y)) );
Timing(jfunc(x1,y1));


    

In [9]:

    

resultsJ1=Timing(jfunc(x1,y1))


    

    
Out[9]:





$$  \left[ 0.005456158,7.485470860550343 \right]  $$

In [10]:

    

jfunc([a+b,c+d],[u+v,y+z])


    

    
Out[10]:





$$ \frac{ \left( a + b \right) ^{2}}{ \left( u + v \right) ^{3}} + \frac{ \left( c + d \right) ^{2}}{ \left( y + z \right) ^{3}} $$

In [23]:

    

Julia();


    

    




LoadError: UndefVarError: Julia not defined
while loading In[23], in expression starting on line 1

In [24]:

    

expr=@sym a+b


    

    
Out[24]:





:a + :b

In [25]:

    

Expand(expr^2)


    

    
Out[25]:





:a^2 + :b^2 + 2:a*:b

In [26]:

    

isymata();


    

In [27]:

    

Julia();


    

In [28]:

    

fj(x,y)=sum(u->u[1]^2/u[2]^3,zip(x,y))


    

    
Out[28]:





fj (generic function with 1 method)

In [29]:

    

isymata();


    

In [30]:

    

fj=J(Main.fj);


    

In [31]:

    

fj(x1,y1)


    

    




MethodError(start,(:x1,))






    




LoadError: MethodError: no method matching start(::Symbol)
Closest candidates are:
  start(!Matched::SimpleVector) at essentials.jl:170
  start(!Matched::Base.MethodList) at reflection.jl:258
  start(!Matched::IntSet) at intset.jl:184
  ...
while loading In[31], in expression starting on line 1

In [32]:

    

J(time)()


    

    
Out[32]:





$$ 1.480639051820034e9 $$

In [33]:

    

y2=J(linspace(1, 1000.0, 1000))


    

    
Out[33]:





$$ linspace(1.0,1000.0,1000) $$

In [34]:

    

jfunc(x1,y1)


    

    
Out[34]:





$$ jfunc \!  \left( x1,y1 \right)  $$

In [35]:

    

resultsJ2=Timing(jfunc(x1,y1))


    

    
Out[35]:





$$  \left[ 7.69e-5,jfunc \!  \left( x1,y1 \right)  \right]  $$

In [36]:

    

[resultsS1[1],resultsS2[1]]/resultsJ1[1]


    

    




MethodError(Symata.get_part_one_ind,(:resultsS1,1))






    




LoadError: MethodError: no method matching get_part_one_ind(::Symbol, ::Int64)
Closest candidates are:
  get_part_one_ind{V<:Union{Array{T,N},Symata.Mxpr{T}}}(!Matched::V<:Union{Array{T,N},Symata.Mxpr{T}}, ::Integer) at /Users/rob/.julia/v0.5/Symata/src/parts.jl:13
  get_part_one_ind(!Matched::Dict{K,V}, ::Any) at /Users/rob/.julia/v0.5/Symata/src/parts.jl:17
  get_part_one_ind(!Matched::Tuple, ::Any) at /Users/rob/.julia/v0.5/Symata/src/parts.jl:18
while loading In[36], in expression starting on line 1

In [37]:

    

jfunc(y2,y2)
resultsJ3=Timing(jfunc(y2,y2))


    

    
Out[37]:





$$  \left[ 4.561e-5,jfunc \!  \left( linspace(1.0,1000.0,1000),linspace(1.0,1000.0,1000) \right)  \right]  $$

In [38]:

    

resultsJ2[1]/resultsJ3[1]


    

    
Out[38]:





$$ 1.6860337645253236 $$

In [39]:

    

g=Compile(x^2)
g(3)


    

    
Out[39]:





$$ 9 $$

In [40]:

    

g=SymataCall(x, x^2);
g(3)


    

    
Out[40]:





$$ 9 $$

In [41]:

    

ex1=Together(PolyLog(-1,z),(1-z))


    

    
Out[41]:





$$ \frac{z}{ \left( -1 + z \right) ^{2}} $$

In [42]:

    

ex1./(z=>3)


    

    
Out[42]:





$$ \frac{3}{4} $$

In [43]:

    

Julia();


    

In [44]:

    

? @symExpr


    

    
Out[44]:





@symExpr(expr)
Symata-evaluates expr, translates the result to a Julia expression, and inserts it into the surrounding code. This works just like any Julia macro for inserting code, except that the code is generated by evaluating a Symata expression.
The following Symata code returns a rational expression, which is used as the body of a Julia function.

f1(z) = @symExpr Together(PolyLog(-1,z),(1-z))

In [45]:

    

f1(z) = @symExpr Together(PolyLog(-1,z),(1-z))


    

    
Out[45]:





f1 (generic function with 1 method)

In [46]:

    

f1(3)


    

    
Out[46]:




3//4

In [89]:

    

isymata();


    

In [90]:

    

y2


    

    
Out[90]:





$$ linspace(1.0,1000.0,1000) $$

In [91]:

    

y3=Unpack(y2);


    

In [92]:

    

[Head(y3),Length(y3), y3[1], y3[-1]]


    

    
Out[92]:





$$  \left[ \text{List},1000,1.0,1000.0 \right]  $$

In [93]:

    

y3==y1==Range(10.0^3)


    

    
Out[93]:





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2.0,853.0,854.0,855.0,856.0,857.0,858.0,859.0,860.0,861.0,862.0,863.0,864.0,865.0,866.0,867.0,868.0,869.0,870.0,871.0,872.0,873.0,874.0,875.0,876.0,877.0,878.0,879.0,880.0,881.0,882.0,883.0,884.0,885.0,886.0,887.0,888.0,889.0,890.0,891.0,892.0,893.0,894.0,895.0,896.0,897.0,898.0,899.0,900.0,901.0,902.0,903.0,904.0,905.0,906.0,907.0,908.0,909.0,910.0,911.0,912.0,913.0,914.0,915.0,916.0,917.0,918.0,919.0,920.0,921.0,922.0,923.0,924.0,925.0,926.0,927.0,928.0,929.0,930.0,931.0,932.0,933.0,934.0,935.0,936.0,937.0,938.0,939.0,940.0,941.0,942.0,943.0,944.0,945.0,946.0,947.0,948.0,949.0,950.0,951.0,952.0,953.0,954.0,955.0,956.0,957.0,958.0,959.0,960.0,961.0,962.0,963.0,964.0,965.0,966.0,967.0,968.0,969.0,970.0,971.0,972.0,973.0,974.0,975.0,976.0,977.0,978.0,979.0,980.0,981.0,982.0,983.0,984.0,985.0,986.0,987.0,988.0,989.0,990.0,991.0,992.0,993.0,994.0,995.0,996.0,997.0,998.0,999.0,1000.0 \right] \text{==}y1 \, \text{&&} \, y1\text{==} \left[ 1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0,11.0,12.0,13.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0,29.0,30.0,31.0,32.0,33.0,34.0,35.0,36.0,37.0,38.0,39.0,40.0,41.0,42.0,43.0,44.0,45.0,46.0,47.0,48.0,49.0,50.0,51.0,52.0,53.0,54.0,55.0,56.0,57.0,58.0,59.0,60.0,61.0,62.0,63.0,64.0,65.0,66.0,67.0,68.0,69.0,70.0,71.0,72.0,73.0,74.0,75.0,76.0,77.0,78.0,79.0,80.0,81.0,82.0,83.0,84.0,85.0,86.0,87.0,88.0,89.0,90.0,91.0,92.0,93.0,94.0,95.0,96.0,97.0,98.0,99.0,100.0,101.0,102.0,103.0,104.0,105.0,106.0,107.0,108.0,109.0,110.0,111.0,112.0,113.0,114.0,115.0,116.0,117.0,118.0,119.0,120.0,121.0,122.0,123.0,124.0,125.0,126.0,127.0,128.0,129.0,130.0,131.0,132.0,133.0,134.0,135.0,136.0,137.0,138.0,139.0,140.0,141.0,142.0,143.0,144.0,145.0,146.0,147.0,148.0,149.0,150.0,151.0,152.0,153.0,154.0,155.0,156.0,157.0,158.0,159.0,160.0,161.0,162.0,163.0,164.0,165.0,166.0,167.0,168.0,169.0,170.0,171.0,172.0,173.0,174.0,175.0,176.0,177.0,178.0,179.0,180.0,181.0,182.0,183.0,184.0,185.0,186.0,187.0,188.0,189.0,190.0,191.0,192.0,193.0,194.0,195.0,196.0,197.0,198.0,199.0,200.0,201.0,202.0,203.0,204.0,205.0,206.0,207.0,208.0,209.0,210.0,211.0,212.0,213.0,214.0,215.0,216.0,217.0,218.0,219.0,220.0,221.0,222.0,223.0,224.0,225.0,226.0,227.0,228.0,229.0,230.0,231.0,232.0,233.0,234.0,235.0,236.0,237.0,238.0,239.0,240.0,241.0,242.0,243.0,244.0,245.0,246.0,247.0,248.0,249.0,250.0,251.0,252.0,253.0,254.0,255.0,256.0,257.0,258.0,259.0,260.0,261.0,262.0,263.0,264.0,265.0,266.0,267.0,268.0,269.0,270.0,271.0,272.0,273.0,274.0,275.0,276.0,277.0,278.0,279.0,280.0,281.0,282.0,283.0,284.0,285.0,286.0,287.0,288.0,289.0,290.0,291.0,292.0,293.0,294.0,295.0,296.0,297.0,298.0,299.0,300.0,301.0,302.0,303.0,304.0,305.0,306.0,307.0,308.0,309.0,310.0,311.0,312.0,313.0,314.0,315.0,316.0,317.0,318.0,319.0,320.0,321.0,322.0,323.0,324.0,325.0,326.0,327.0,328.0,329.0,330.0,331.0,332.0,333.0,334.0,335.0,336.0,337.0,338.0,339.0,340.0,341.0,342.0,343.0,344.0,345.0,346.0,347.0,348.0,349.0,350.0,351.0,352.0,353.0,354.0,355.0,356.0,357.0,358.0,359.0,360.0,361.0,362.0,363.0,364.0,365.0,366.0,367.0,368.0,369.0,370.0,371.0,372.0,373.0,374.0,375.0,376.0,377.0,378.0,379.0,380.0,381.0,382.0,383.0,384.0,385.0,386.0,387.0,388.0,389.0,390.0,391.0,392.0,393.0,394.0,395.0,396.0,397.0,398.0,399.0,400.0,401.0,402.0,403.0,404.0,405.0,406.0,407.0,408.0,409.0,410.0,411.0,412.0,413.0,414.0,415.0,416.0,417.0,418.0,419.0,420.0,421.0,422.0,423.0,424.0,425.0,426.0,427.0,428.0,429.0,430.0,431.0,432.0,433.0,434.0,435.0,436.0,437.0,438.0,439.0,440.0,441.0,442.0,443.0,444.0,445.0,446.0,447.0,448.0,449.0,450.0,451.0,452.0,453.0,454.0,455.0,456.0,457.0,458.0,459.0,460.0,461.0,462.0,463.0,464.0,465.0,466.0,467.0,468.0,469.0,470.0,471.0,472.0,473.0,474.0,475.0,476.0,477.0,478.0,479.0,480.0,481.0,482.0,483.0,484.0,485.0,486.0,487.0,488.0,489.0,490.0,491.0,492.0,493.0,494.0,495.0,496.0,497.0,498.0,499.0,500.0,501.0,502.0,503.0,504.0,505.0,506.0,507.0,508.0,509.0,510.0,511.0,512.0,513.0,514.0,515.0,516.0,517.0,518.0,519.0,520.0,521.0,522.0,523.0,524.0,525.0,526.0,527.0,528.0,529.0,530.0,531.0,532.0,533.0,534.0,535.0,536.0,537.0,538.0,539.0,540.0,541.0,542.0,543.0,544.0,545.0,546.0,547.0,548.0,549.0,550.0,551.0,552.0,553.0,554.0,555.0,556.0,557.0,558.0,559.0,560.0,561.0,562.0,563.0,564.0,565.0,566.0,567.0,568.0,569.0,570.0,571.0,572.0,573.0,574.0,575.0,576.0,577.0,578.0,579.0,580.0,581.0,582.0,583.0,584.0,585.0,586.0,587.0,588.0,589.0,590.0,591.0,592.0,593.0,594.0,595.0,596.0,597.0,598.0,599.0,600.0,601.0,602.0,603.0,604.0,605.0,606.0,607.0,608.0,609.0,610.0,611.0,612.0,613.0,614.0,615.0,616.0,617.0,618.0,619.0,620.0,621.0,622.0,623.0,624.0,625.0,626.0,627.0,628.0,629.0,630.0,631.0,632.0,633.0,634.0,635.0,636.0,637.0,638.0,639.0,640.0,641.0,642.0,643.0,644.0,645.0,646.0,647.0,648.0,649.0,650.0,651.0,652.0,653.0,654.0,655.0,656.0,657.0,658.0,659.0,660.0,661.0,662.0,663.0,664.0,665.0,666.0,667.0,668.0,669.0,670.0,671.0,672.0,673.0,674.0,675.0,676.0,677.0,678.0,679.0,680.0,681.0,682.0,683.0,684.0,685.0,686.0,687.0,688.0,689.0,690.0,691.0,692.0,693.0,694.0,695.0,696.0,697.0,698.0,699.0,700.0,701.0,702.0,703.0,704.0,705.0,706.0,707.0,708.0,709.0,710.0,711.0,712.0,713.0,714.0,715.0,716.0,717.0,718.0,719.0,720.0,721.0,722.0,723.0,724.0,725.0,726.0,727.0,728.0,729.0,730.0,731.0,732.0,733.0,734.0,735.0,736.0,737.0,738.0,739.0,740.0,741.0,742.0,743.0,744.0,745.0,746.0,747.0,748.0,749.0,750.0,751.0,752.0,753.0,754.0,755.0,756.0,757.0,758.0,759.0,760.0,761.0,762.0,763.0,764.0,765.0,766.0,767.0,768.0,769.0,770.0,771.0,772.0,773.0,774.0,775.0,776.0,777.0,778.0,779.0,780.0,781.0,782.0,783.0,784.0,785.0,786.0,787.0,788.0,789.0,790.0,791.0,792.0,793.0,794.0,795.0,796.0,797.0,798.0,799.0,800.0,801.0,802.0,803.0,804.0,805.0,806.0,807.0,808.0,809.0,810.0,811.0,812.0,813.0,814.0,815.0,816.0,817.0,818.0,819.0,820.0,821.0,822.0,823.0,824.0,825.0,826.0,827.0,828.0,829.0,830.0,831.0,832.0,833.0,834.0,835.0,836.0,837.0,838.0,839.0,840.0,841.0,842.0,843.0,844.0,845.0,846.0,847.0,848.0,849.0,850.0,851.0,852.0,853.0,854.0,855.0,856.0,857.0,858.0,859.0,860.0,861.0,862.0,863.0,864.0,865.0,866.0,867.0,868.0,869.0,870.0,871.0,872.0,873.0,874.0,875.0,876.0,877.0,878.0,879.0,880.0,881.0,882.0,883.0,884.0,885.0,886.0,887.0,888.0,889.0,890.0,891.0,892.0,893.0,894.0,895.0,896.0,897.0,898.0,899.0,900.0,901.0,902.0,903.0,904.0,905.0,906.0,907.0,908.0,909.0,910.0,911.0,912.0,913.0,914.0,915.0,916.0,917.0,918.0,919.0,920.0,921.0,922.0,923.0,924.0,925.0,926.0,927.0,928.0,929.0,930.0,931.0,932.0,933.0,934.0,935.0,936.0,937.0,938.0,939.0,940.0,941.0,942.0,943.0,944.0,945.0,946.0,947.0,948.0,949.0,950.0,951.0,952.0,953.0,954.0,955.0,956.0,957.0,958.0,959.0,960.0,961.0,962.0,963.0,964.0,965.0,966.0,967.0,968.0,969.0,970.0,971.0,972.0,973.0,974.0,975.0,976.0,977.0,978.0,979.0,980.0,981.0,982.0,983.0,984.0,985.0,986.0,987.0,988.0,989.0,990.0,991.0,992.0,993.0,994.0,995.0,996.0,997.0,998.0,999.0,1000.0 \right]  $$

In [52]:

    

y3[1]="cat"


    

    
Out[52]:





$$ \text{"cat"} $$

In [53]:

    

y3[1:10]


    

    
Out[53]:





$$  \left[ \text{"cat"},2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0 \right]  $$

In [54]:

    

y4=J(collect)(y2);


    

In [55]:

    

[Head(y4), y4[1]]


    

    
Out[55]:





$$  \left[ \text{Array{Float64,1}},1.0 \right]  $$

In [56]:

    

y5=J(mxpr(:List, Any[collect(linspace(1.0, 1000,1000))...]));


    

In [57]:

    

[Head(y5), y5[-1]]


    

    
Out[57]:





$$  \left[ \text{List},1000.0 \right]  $$

In [58]:

    

y5=J(mxpr(:List, Any[collect(1.0:1.0:1000.0)...]));


    

In [59]:

    

[Head(y1),Head(y3)]


    

    
Out[59]:





$$  \left[ \text{Symbol},\text{List} \right]  $$

In [60]:

    

y6=Pack(y1)
y7=Pack(y3);


    

    




MethodError(Symata.margs,(:y1,))






    




LoadError: MethodError: no method matching margs(::Symbol)
Closest candidates are:
  margs(!Matched::Symata.Mxpr{T}) at /Users/rob/.julia/v0.5/Symata/src/mxpr_type.jl:403
  margs(!Matched::Dict{K,V}) at /Users/rob/.julia/v0.5/Symata/src/mxpr_type.jl:411
while loading In[60], in expression starting on line 1

In [61]:

    

[Head(y6),Head(y7)]


    

    
Out[61]:





$$  \left[ \text{Symbol},\text{Symbol} \right]  $$

In [62]:

    

Julia();


    

In [63]:

    

? @sym


    

    
Out[63]:





@sym expr
Embed symata expression expr in Julia code.
Read and evaluate expr embedded in Julia code.

julia> a = 1       # Julia symbol `a`
julia> @sym a = 2  # Symata symbol
julia> a
1
julia> @sym a
2

In [64]:

    

? symparsestring


    

    




search: symparsestring







    
Out[64]:





symparsestring(s::String)
parses s into one or more Julia expressions, translates each one to a Symata expression, and returns an array of the Symata expressions.
Note that the phrases Symata expression and Julia expression here include numbers, symbols, etc.

In [65]:

    

? symeval


    

    




search: symeval symparseeval symtranseval







    
Out[65]:





symeval(expr::Any)
send expr through the Symata evaluation sequence. expr is an Mxpr or number, symbol, etc.
In particular, an Expr (i.e. not translated to Symata) Symata-evaluated (whic in this case means returned unchanged) by the Symata evaluation sequence.

In [66]:

    

@sym z="cat"


    

    
Out[66]:





"cat"

In [67]:

    

z


    

    




LoadError: UndefVarError: z not defined
while loading In[67], in expression starting on line 1

In [68]:

    

@sym z


    

    
Out[68]:





"cat"

In [69]:

    

unpacktoList(1:2:7)


    

    
Out[69]:





[1,3,5,7]

In [70]:

    

@sym a=3


    

    
Out[70]:




3

In [71]:

    

scode=parse("Sqrt(a)")


    

    
Out[71]:





:(Sqrt(a))

In [72]:

    

res=symtranseval(scode)


    

    
Out[72]:





3^(1//2)

In [73]:

    

function squareroots()
    a = (i for i in 1:9)
    setsymata(:a, unpacktoList(a))
    symprintln(symparseeval("Sqrt(a)"))
    nothing
end


    

    
Out[73]:





squareroots (generic function with 1 method)

In [74]:

    

squareroots()


    

    




[1,2^(1/2),3^(1/2),2,5^(1/2),2^(1/2)*3^(1/2),7^(1/2),22^(1/2),3]

In [75]:

    

isymata();


    

In [76]:

    

ToJuliaString(3*x^2*y^3+Cos(1))


    

    
Out[76]:





$$ \text{"3 * x ^ 2 * y ^ 3 + cos(1)"} $$

In [77]:

    

s2 = ToJuliaString(3*x^2*y^3+Cos(1), NoSymata=>False)


    

    
Out[77]:





$$ \text{"mplus(mmul(3,mpow(x,2),mpow(y,3)),Cos(1))"} $$

In [78]:

    

SetJ(s2,s2)


    

    
Out[78]:





$$ \text{"mplus(mmul(3,mpow(x,2),mpow(y,3)),Cos(1))"} $$

In [79]:

    

J(x=3,y=2)
J(eval(parse(Main.s2)))


    

    
Out[79]:





$$ 216 + \text{Cos} \!  \left( 1 \right)  $$

In [80]:

    

Julia()


    

In [81]:

    

Julia()


    

    




LoadError: UndefVarError: Julia not defined
while loading In[81], in expression starting on line 1

In [82]:

    

isymata()


    

In [ ]:

    




    

In [83]:

    

l = [1, 2, 3]


    

    
Out[83]:





$$  \left[ 1,2,3 \right]  $$

In [84]:

    

Head(l)


    

    
Out[84]:





$$ \text{List} $$

In [85]:

    

Julia()


    

In [86]:

    

a=getsymata(a)


    

    




LoadError: UndefVarError: a not defined
while loading In[86], in expression starting on line 1

In [ ]: