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Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, e, l
from proveit.numbers import Add, Exp, Interval, Mult, Sum, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import Pfail, _two_pow__t_minus_one
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Pfail(e), Add(Mult(frac(one, two), Sum(index_or_indices = [l], summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), subtract(_two_pow__t_minus_one, one)))), Mult(frac(one, four), frac(one, Exp(e, two)))))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\left[P_{\rm fail}\right]\left(e\right), \left(\frac{1}{2} \cdot \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right) + \left(\frac{1}{4} \cdot \frac{1}{e^{2}}\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 3
operand: 42
2Operationoperator: 48
operands: 5
3Literal
4ExprTuple42
5ExprTuple6, 7
6Operationoperator: 9
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple13, 14
11Operationoperator: 28
operands: 15
12Operationoperator: 16
operand: 20
13Operationoperator: 28
operands: 18
14Operationoperator: 28
operands: 19
15ExprTuple54, 46
16Literal
17ExprTuple20
18ExprTuple54, 21
19ExprTuple54, 22
20Lambdaparameter: 37
body: 24
21Literal
22Operationoperator: 44
operands: 25
23ExprTuple37
24Conditionalvalue: 26
condition: 27
25ExprTuple42, 46
26Operationoperator: 28
operands: 29
27Operationoperator: 30
operands: 31
28Literal
29ExprTuple54, 32
30Literal
31ExprTuple37, 33
32Operationoperator: 44
operands: 34
33Operationoperator: 35
operands: 36
34ExprTuple37, 46
35Literal
36ExprTuple38, 39
37Variable
38Operationoperator: 48
operands: 40
39Operationoperator: 48
operands: 41
40ExprTuple42, 54
41ExprTuple43, 51
42Variable
43Operationoperator: 44
operands: 45
44Literal
45ExprTuple46, 47
46Literal
47Operationoperator: 48
operands: 49
48Literal
49ExprTuple50, 51
50Literal
51Operationoperator: 52
operand: 54
52Literal
53ExprTuple54
54Literal