logo

Expression of type InSet

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 l
from proveit.logic import InSet
from proveit.numbers import Exp, Real, Sum, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain
In [2]:
# build up the expression from sub-expressions
expr = InSet(Sum(index_or_indices = [l], summand = frac(one, Exp(_diff_l_scaled_delta_floor, two)), domain = _pos_domain), Real)
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(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) \in \mathbb{R}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 13
operands: 1
1ExprTuple2, 3
2Operationoperator: 4
operand: 6
3Literal
4Literal
5ExprTuple6
6Lambdaparameter: 26
body: 8
7ExprTuple26
8Conditionalvalue: 9
condition: 10
9Operationoperator: 11
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple41, 15
13Literal
14ExprTuple26, 16
15Operationoperator: 42
operands: 17
16Operationoperator: 18
operands: 19
17ExprTuple20, 46
18Literal
19ExprTuple21, 22
20Operationoperator: 31
operands: 23
21Operationoperator: 31
operands: 24
22Operationoperator: 42
operands: 25
23ExprTuple26, 27
24ExprTuple28, 41
25ExprTuple46, 29
26Variable
27Operationoperator: 37
operand: 33
28Variable
29Operationoperator: 31
operands: 32
30ExprTuple33
31Literal
32ExprTuple47, 34
33Operationoperator: 35
operands: 36
34Operationoperator: 37
operand: 41
35Literal
36ExprTuple39, 40
37Literal
38ExprTuple41
39Operationoperator: 42
operands: 43
40Operationoperator: 44
operand: 48
41Literal
42Literal
43ExprTuple46, 47
44Literal
45ExprTuple48
46Literal
47Literal
48Literal