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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, k, m
from proveit.numbers import Exp, Mult, Neg, Sum, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _t, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Exp(frac(one, Exp(two, frac(_t, two))), two), Sum(index_or_indices = [k], summand = Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))), domain = _m_domain))
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(\frac{1}{2^{\frac{t}{2}}}\right)^{2}, \sum_{k = 0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\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: 48
operands: 3
2Operationoperator: 4
operand: 7
3ExprTuple6, 54
4Literal
5ExprTuple7
6Operationoperator: 39
operands: 8
7Lambdaparameter: 52
body: 10
8ExprTuple45, 11
9ExprTuple52
10Conditionalvalue: 12
condition: 13
11Operationoperator: 48
operands: 14
12Operationoperator: 46
operands: 15
13Operationoperator: 16
operands: 17
14ExprTuple54, 18
15ExprTuple19, 20
16Literal
17ExprTuple52, 21
18Operationoperator: 39
operands: 22
19Operationoperator: 48
operands: 23
20Operationoperator: 48
operands: 24
21Operationoperator: 25
operands: 26
22ExprTuple55, 54
23ExprTuple28, 27
24ExprTuple28, 29
25Literal
26ExprTuple30, 31
27Operationoperator: 46
operands: 32
28Literal
29Operationoperator: 41
operand: 37
30Literal
31Operationoperator: 34
operands: 35
32ExprTuple54, 50, 51, 36, 52
33ExprTuple37
34Literal
35ExprTuple44, 38
36Literal
37Operationoperator: 39
operands: 40
38Operationoperator: 41
operand: 45
39Literal
40ExprTuple43, 44
41Literal
42ExprTuple45
43Operationoperator: 46
operands: 47
44Operationoperator: 48
operands: 49
45Literal
46Literal
47ExprTuple54, 50, 51, 52, 53
48Literal
49ExprTuple54, 55
50Literal
51Literal
52Variable
53Variable
54Literal
55Literal