# from the theory of proveit.numbers.summation¶

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.
# import Expression classes needed to build the expression
from proveit import a, b, c, k
from proveit.core_expr_types import alpha_k
from proveit.numbers import Add, Interval, Sum, one

In [2]:
# build up the expression from sub-expressions
sub_expr1 = [k]
expr = Add(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(Add(b, one), c)))

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_{k = a}^{b} \alpha_{k}\right) + \left(\sum_{k = b + 1}^{c} \alpha_{k}\right)

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',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 28
operands: 1
1ExprTuple2, 3
2Operationoperator: 5
operand: 7
3Operationoperator: 5
operand: 8
4ExprTuple7
5Literal
6ExprTuple8
7Lambdaparameter: 20
body: 9
8Lambdaparameter: 20
body: 10
9Conditionalvalue: 12
condition: 11
10Conditionalvalue: 12
condition: 13
11Operationoperator: 17
operands: 14
12IndexedVarvariable: 15
index: 20
13Operationoperator: 17
operands: 18
14ExprTuple20, 19
15Variable
16ExprTuple20
17Literal
18ExprTuple20, 21
19Operationoperator: 23
operands: 22
20Variable
21Operationoperator: 23
operands: 24
22ExprTuple25, 30
23Literal
24ExprTuple26, 27
25Variable
26Operationoperator: 28
operands: 29
27Variable
28Literal
29ExprTuple30, 31
30Variable
31Literal